ypj 
11 


WORKS   OF   JOHN   S.  REID 


PUBLISHED    BY 


JOHN  WILEY  &  SONS,    INC. 


A  Course  in  Mechanical  Drawing:. 

Third  Edition,  Revised  and  Enlarged.  &ro, 
viii+  186  pages,  233  figures.  Cloth,  $2.00. 

Mechanical     Drawing:    and     Elementary    Machine 
Design. 

By  John  S.  Reid,  Professor  of  Mechanical  Draw- 
ing, Armour  Institute  of  Technology,  and  David 
Reid,  formerly  Instructor  in  Mechanical  Drawing, 
Sibley  College,  Cornell  University.  Second 
Edition  Revised  and  Enlarged.  8vo,  xii+439 
pages,  329  figures.  Cloth,  $3.00. 


MECHANICAL  DRAWING 


By 

JOHN  S.  REID,  Sr.,  Mem.A.S.M.E. 

Assistant  Professor  of  Mechanical  and  Elementary  Machine  Drawing, 
Armour  Institute  of  Technology,  Chicago,  III. 


FIRST    EDITION 


NEW  YORK 

JOHN   WILEY   &   SONS,    INC. 

LONDON:  CHAPMAN  &  HALL,  LIMITED 

1919 


Copyright,  1919 

BY 
JOHN  S.  REID,  SR. 


PRESS  OF 

RRAUNWORTH    &   CO. 

BOOK  MANUFACTURERS 

BROOKLYN.   N.  Y. 


PREFACE 


A  MECHANICAL  DRAWING  is  used  to  convey  precise  information 
from  one  person  to  another. 

A  patternmaker  must  have  a  true  drawing  of  an  object, 
giving  correct  dimensions  and  instructions  before  he  can  make 
a  pattern,  from  which  the  foundryman  can  make  a  rough  casting. 

The  machinist  must  have  a  drawing  from  which  he  can 
obtain  accurate  information  to  enable  him  to  take  the  rough 
casting  and  by  slotting,  planing,  drilling,  grinding,  chipping 
or  turning  he  can  produce  the  finished  article  as  designed  by 
the  draftsman. 

Contractors,  builders,  architects,  and  engineers  of  all  kinds, 
must  have  accurate  drawings  to  enable  them  to  produce  satis- 
factory results  in  their  work. 

To  do  this  it  is  essential  that  working  drawings  should 
be  made  according  to  certain  principles  and  methods  thoroughly 
understood  by  the  man  who  makes  the  drawing  and  the  man 
who  uses  it. 

This  volume  on  Mechanical  Drawing  is  a  fundamental 
course  embodying  all  the  theory,  principles,  and  methods 
necessary  to  enable  the  student  to  make  a  practical  working 
drawing. 

Considering  Mechanical  Drawing  as  a  language  to  convey 
thoughts  and  ideas ;  orthographic  projection,  which  is  a  division 
of  descriptive  geometry,  is  its  grammar  and  the  foundation  upon 
which  is  built  all  kinds  of  correct  mechanical  drawings. 

This  course  is  the  result  of  twenty-five  years  of  experience 
in  teaching  Mechanical  Drawing  and  Elementary  Machine 
Drafting  (fifteen  years  at  Cornell  University  and  nearly  eleven 
years  at  Armour  Institute  of  Technology,  besides  Summer  School 

iii 

416876 


iv  PREFACE 

and  Evening  Classes)  and  twenty  years  of  designing  and  drafting 
in  practical  work. 

In  1898,  while  at  Cornell  University,  the  writer  produced  a 
book  on  Mechanical  Drawing  entitled  "A  Course  in  Mechanical 
Drawing."  In  1910  it  was  enlarged  by  adding  short  courses 
in  Architectural  Drawing,  Sheet  Metal  Drafting  and  Elementary 
Machine  Drawing.  The  present  volume  is  offered,  in  the  light 
of  the  above  experience,  as  a  complete  course,  not  too  long, 
preparatory  to  college  work  and  as  a  foundation  to  practical 
drafting. 

The  divisions  of  the  work  included  in  the  following  course 
should  be  standard  because  they  are  all  needed  in  the  further 
development  of  draftsmanship.  If  any  divisions  should  be 
emphasized  more  than  others  they  are  freehand  lettering,  ortho- 
graphic projection  and  isometrical  drawing. 

This  course  is  preparatory  to  a  course  in  "  Elementary  Ma- 
chine Drafting"  by  the  writer  soon  to  be  issued  from  the  press 
of  John  Wiley  &  Sons,  Scientific  Publishers,  New  York. 

JOHN  S.  REID,  SR. 

ARMOUR  INSTITUTE  OF  TECHNOLOGY, 
Chicago,  111.,  Feb.,  1919. 


CONTENTS 


CHAPTER  I 

ARTICLE     PAGE 

INSTRUMENTS  AND  THEIR  USES i  i 

Drawing  Board i  i 

T-square 2  i 

Triangles 3  4 

Pencil 4  7 

Pocket  Case  of  Instruments 5  9 

Large  Compasses 6  10 

Spring  Bow  Instruments 7  12 

Large  Dividers  or  Spacers 8  13 

Straight  Line  Pen 9  14 

Sharpening  the  Pens : 10  15 

Triangular  Scale n  16 

Protractor 12  18 

Irregular  Curve 13  19 

Emery  Pencil  Pointer 14  19 

Soft  Rubber  Eraser 15  19 

Erasing  Shield. 16  20 

Art  Gum 17  20 

Ink 17  21 

Thumb  Tacks 17  21 

Cross-section  Pad 18  21 

Drawing  Paper 18  21 

Tracing  Cloth 18  21 

CHAPTER  II 
DRAFTING  ROOM  CONVENTIONS 19-30      21-  43 

CHAPTER  III 
FREEHAND  LETTERING  AND  GEOMETRIC  DRAWING 31-38      44-  80 

CHAPTER  IV 

ORTHOGRAPHIC  PROJECTION 39-43      81-  88 

v 


vi  CONTENTS 

CHAPTER  V 

ARTICLE  PAGE 

REPRESENTATION  OF  POINTS  AND  LINES 44-53        89-99 

CHAPTER  VI 
REPRESENTATION  OF  PLANES 54-65    100-108 

CHAPTER  VII 
ORTHOGRAPHIC  PROJECTION  APPLIED 66-73    109-127 

f' 

CHAPTER  VIII 

ISOMETRICAL  PROJECTION 74-82      128-144 

CHAPTER  IX 
WORKING  DRAWINGS 83-85    145-156 

APPENDIX  TO  THE  REQUIRED   COURSE  IN 

MECHANICAL  DRAWING 157-210 

LETTERING,  Continued 157-162 

GEOMETRICAL  DRAWING,  Continued 87  163 

SHADE  LINES,  SHADES  AND  SHADOWS 194 

CONIC  SECTIONS 208 

PRESENT  PRACTICE  IN  DRAFTING  ROOM  CONVENTIONS  AND  METHODS  IN 

MAKING  PRACTICAL  WORKING  DRAWINGS 215 


INTRODUCTION 


THE  following  course  is  designed  to  train  young  men,  who 
have  satisfactorily  completed  the  course  in  Mechanical  Drawing, 
to  become  practical  detail  draftsmen  and  to  lay  a  proper  founda- 
tion for  a  future  course  in  Machine  Design. 

It  is  the  part  of  the  detail  draftsman  to  make  the  commercial 
working  drawings  of  machine  details  for  the  use  of  the  workmen 
in  the  shop. 

This  is  usually  done  under  the  direction  of  the  main 
draftsman  who  has  charge  of  the  design  and  construction  of 
the  whole  machine. 

In  mechanical  drawing,  the  student  learned  to  make  correct 
drawings  of  objects  embodying  the  principles  of  orthographic 
projection  or  theory  of  drawing  without  much  regard  to  the  use 
of  the  objects  drawn. 

In  machine  drawing,  however,  more  than  this  is  required. 
The  draftsman's  motive  in  making  a  working  drawing  is  to 
convey  information  by  means  of  it  to  the  men  in  the  shop  and, 
therefore,  the  drawing  must  be  first  correct,  second,  it  must  be 
made  in  as  short  a  time  as  possible  consistent  with  correctness 
and  third,  it  must  be  as  neat  and  well  drawn  as  the  first  and 
second  requirements  will  permit. 

Correctness.  This  cannot  be  emphasized  too  much.  A 
drawing  that  is  not  correct  in  every  particular  is  not  good  for 
much  and,  in  some  cases,  worse  than  useless,  causing  serious 
loss  of  time  and  material. 

The  writer  recalls  a  case  in  point  in  which  the  drawing  of  one 
of  a  set  of  boiler  plates  contained  a  wrong  dimension.  The 
order  was  for  thirty  locomotives  to  be  delivered  on  a  certain 
date  under  penalty.  The  thirty  wrong  plates  had  to  be  thrown 
out  and  others  ordered.  The  work  was  held  up  with  serious  loss 

vii 


viii  INTRODUCTION 

of  time,  labor  and  material.  The  draftsman  who  made  the 
blunder  was  discharged. 

In  addition  to  the  correct  mechanical  drawing  of  the  machine 
the  drawing  must  contain  all  correct  dimensions,  notes,  pattern 
numbers,  finishes,  etc. 

In  placing  dimensions  on  a  drawing,  the  draftsman  should 
be  able  to  put  himself  in  the  position  of  the  workman  who  is  to 
use  it,  and  place  the  dimensions  as  far  as  possible  where  the  work- 
man would  be  most  likely  to  look  for  them,  this  makes  it  easier 
to  read  the  drawing  and  saves  the  workman's  time. 

There  is  always  an  inclination  on  the  part  of  certain  students 
in  solving  problems  to  copy  the  illustrations  in  the  text,  the 
finished  drawings  of  other  students  or  importune  the  Instructor 
to  tell  them  just  what  to  do  without  much  effort  or  thought  on 
their  own  part. 

This  is  a  great  mistake  on  the  students  part,  for,  beyond  the 
practice  in  mechanical  drawing,  he  gets  very  little  out  of  his 
machine-drawing  course  unless  he  realizes  the  design  and  con- 
struction of  the  machine  he  is  drawing,  why  it  is  made  so  and 
not  otherwise,  how  it  is  produced  in  the  pattern  shop,  the 
foundry  and  finished  in  the  machine  shop,  and  put  together  on 
the  erecting  or  assembling  floor. 

He  should  realize  that  the  more  he  learns  of  the  form,  pro- 
portion and  construction  of  the  elements  of  machines  contained 
in  this  course,  the  better  foundation  he  will  lay  for  his  develop- 
ment as  a  designer  of  machines. 

The  young  man  who  takes  full  advantage  of  this  course,  in 
Elementary  Machine  Drafting,  will  fit  himself  as  a  detail  drafts- 
man able  to  make  commercial  working  drawings,  and  such 
ability  will  always  be  in  demand  at  a  good  salary. 

It  is  such  work  the  young  engineer  is  given  to  do  first  after 
graduation,  and  when  he  has  been  tested  and  his  ability  proved 
he  is  given  more  important  and  responsible  work  to  do. 

The  principles  of  projection  in  the  third  angle  (as  given  in 
Mechanical  Drawing)  will  be  used  exclusively  in  making  all 
drawings. 


MECHANICAL  DRAWING 


CHAPTER   I 

INSTRUMENTS  AND  THEIR  USES 

i.  The  Drawing  Board  should  be  light  for  convenience  in 
handling;  material  soft  pine,  constructed  three-ply  to  pre- 
vent warping.  The  required  size  for  this  course  is  i6"X2i" 
Xft".  '. 

" •> 

\ 


FIG.  i. 

Fig.  i  shows  a  drawing  board  that  has  given  satisfaction 
in  extensive  use. 

The  left-hand  edge  should  be  true  and  square  with  the 
upper  edge.  It  is  not  essential  that  the  other  edges  should 
be  perfectly  square. 

One  face  should  be  selected  for  the  top  face  on  which 
the  drawing  paper  is  to  be  pinned  and  when  the  left-hand 
edge  has  been  made  smooth  and  true  it  should  be  marked 
and  always  used  for  the  T-square  edge. 

2.  The  T-square  should  be  the  same  length  as  the  board, 
viz.,  21".  There  are  many  styles  of  T-squares  made  in  dif- 
ferent materials,  but  a  well-made  pearwood  T-square  with 
fixed  head  is  comparatively  low  priced  and  quite  suitable 


2         .   .  .  ..  ,.:  ...-MECHANICAL  DRAWING 

for  this  work.  The  position  at  the  drawing  table  when  using 
the  T-square  is  of  some  importance.  As  a  rule  the  drafts- 
man should  stand  when  pencilling  in  a  drawing.  It  gives 
him  more  freedom  in  the  use  of  his  tools,  saves  time  and 
is  healthier  than  sitting  crouched  together  on  a  stool. 

When  placing  dimensions,  lettering,  notes,  titles,  bills  of 
material  or  tracing,  it  is  quite  proper  to  sit  on  a  stool  of  con- 
venient height  to  give  a  good  easy  position  when  at  work. 


FIG.  2. 

Most  students,  however,  prefer  to  sit  down  when  drawing 
at  all  times  and  some  have  good  reasons  for  doing  so,  such  as 
"  tired  "  from  standing  so  much  in  laboratory  and  shop  work, 
"  weak  back,"  "  feet  hurt,"  etc. 

A  good  easy  position  should  be  obtained  when  sitting 
down  to  draw  with  the  light  coming  in  from  the  left.  See 
Figs.  2  and  3. 

When  drawing  horizontal,  straight  lines  the  head  of  the 
T-square  should  be  held  rigidly  against  the  left-hand  edge 
of  the  drawing  board,  as  shown  in  Fig.  3. 

Horizontal  straight  lines  should  be  drawn  with  the  pencil 
held  in  a  plane  perpendicular  to  the  board,  passing  through 
the  edge  of  the  T-square  and  making  an  angle  of  about 


INSTRUMENTS  AND  THEIR  USES  3 

60°    with    the    board.      This    angle    should    be  maintained 

throughout    the    line,    and    drawn    from    left    to  right.     See 
Fig.  4. 


"'FRENCH" 


FIG.  3. 


"PHI UPS  AND  ORTH" 


FIG.  4. 


MECHANICAL  DRAWING 


3.  The    Triangles,    one   3o°X6o°Xio"    long   and   45°X8' 
long,  like  those  shown  in  Fig.  5. 


FIG.  5. 

The  material  of  the  triangles  should  be  celluloid;  it  is 
comparatively  cleaner  and  more  durable  than  wood  or 
black  rubber. 


The  triangles  shown  at  Fig.  50  have  rabbeted  edges; 
they  were  devised  to  raise  the  working  edge  from  the  paper 
to  prevent  blots  when  drawing  ink  lines  to  join  other  lines 
already  inked.  When  drawing  an  ink  line  with  the  ordinary 


INSTRUMENTS  AND  THEIR  USES  5 

triangle,  which  is  usually  quite  thin,  great  care  must  be 
observed  when  approaching  another  ink  line  at  the  end  of 
the  stroke,  for  unless  the  pen  is  quickly  lifted  from  the  paper 
as  soon  as  it  touches  the  line  already  inked,  the  ink  in  the 
pen  seems  to  be  drawn  into  the  triangle,  spreading  under 
it  and  causing  a  bad  smear.  The  raised  edge  prevents  this. 
All  vertical  lines  should  be  drawn  with  the  triangles  and 
T-square,  holding  the  pencil  as  explained  in  Art.  2.  See 
Fig.  6. 


FIG.  6.* 

With  the  T-square,  the  3o°X6o°  and  45°  triangles,  various 
angles  may  be  drawn  as  shown  in  Fig.  7. 

At  the  right  in  Fig.  7,  is  shown  how  a  hexagon  may  be 
drawn  circumscribing  a  circle. 

This  is  the  method  used  in  drawing  hexagonal  bolt-heads 
and  nuts. 

With  the  two  triangles,  parallel  lines  may  be  drawn  to 
any  given  line  as  follows: 

Place  one  edge  of  a  triangle  even  with  the  given  line, 
then  place  the  long  edge  of  the  other  triangle  against  another 
edge  of  the  first  triangle,  and  holding  the  second  triangle 
firmly  in  position,  slide  the  first  triangle  against  the  second 

*  From  French's  Engineering  Drawing. 


6  MECHANICAL  DRAWING 

and  any  number  of  parallel  lines  may  be  drawn  to  the  given 
line.     See  Fig.  8. 


FIG.  7. 


FIG.  8. 


Lines  perpendicular  to  given  lines  may  be  drawn  with 
the  triangles  in  a  similar  manner. 

Parallel  lines  and  perpendiculars  may  also  be  drawn  with 
the  T-square  and  one  triangle. 


INSTRUMENTS  AND  THEIR  USES  7 

4.  The  Pencil.  Designs  of  all  kinds  are  usually  worked  out 
in  pencil  first,  and  if  to  be  finished  and  kept  they  are  inked 
in  and  sometimes  shaded;  but  if  the  drawing  is  only  to  be 
finished  in  pencil,  then  all  the  lines  except  construction, 
center,  and  dimension  lines  should  be  made  broad  and  dark, 
so  that  the  drawing  will  stand  out  clear  and  distinct.  It 
will  be  noticed  that  this  calls  for  two  kinds  of  pencil-lines, 


FIG.  9. 

the  first  a  thin,  even  line  made  with  a  hard,  fine-grained  lead 
pencil,  not  less  than  6H  (either  Koh-i-noor  or  "Eldorado"),  and 
sharpened  to  a  knife-edge  in  the  following  manner:  The 
lead  should  be  carefully  bared  of  the  wood  with  a  knife 
for  about  J",  and  the  wood  neatly  tapered  back  from  that 
point  about  J";  then  lay  the  lead  upon  the  emery-paper 
sharpener  illustrated  in  Fig.  9  and  carefully  rub  to  and  fro 
until  the  pencil  assumes  a  long  taper  from  the  wood  to  the 
point;  now  turn  it  over  and  do  the  same  with  the  other 
side,  using  toward  the  last  a  slightly  oscillating  motion  on 
both  sides  until  the  point  has  assumed  a  sharp,  thin,  knife- 
edge  endwise  and  an  elliptical  contour  the  other  way. 

This  point  should  then  be  polished  on  a  piece  of  scrap 
drawing-paper  until  the  rough  burr  left  by  the  emery-paper 
is  removed,  leaving  a  smooth,  keen,  ideal  pencil-point  for 
drawing  straight  lines.  See  A  and  B,  Fig.  10. 


8 


MECHANICAL  DRAWING 


With  such  a  point  but  little  pressure  is  required  in  the 
hands  of  the  draftsman  to  draw  the  most  desirable  line,  one 
that  can  be  easily  erased  when  necessary  and  inked  in  to 
much  better  advantage  than  if  the  line  had  been  made  with 
a  blunt  point,  because,  when  the  pencil-point  is  blunt  the 


FIG.  10. 

inclination  is  to  press  hard  upon  it  when  drawing  a  line. 
This  forms  a  groove  in  the  paper  which  makes  it  very  dif- 
ficult to  draw  an  even  inked  line. 

The  second  kind  of  a  pencil-line  is  the  broad  line,  as  ex- 
plained above;  it  should  be  drawn  with  a  somewhat  softer 
pencil,  say  4H,  and  a  conical  point. 


FIG.  ii. 

The  operations  for  sharpening  the  4H  pencil  are  the  same 
as  for  the  6H,  except  that  instead  of  rubbing  flat,  the  pencil 
should  be  rotated  in  the  fingers  while  it  is  being  rubbed  to 
and  fro  on  the  pointer  (see  Fig.  n),  pressing  slightly  toward 
the  point  so  as  to  form  a  conical-shaped  point.  The  point 
should  not  be  sharp,  like  a  needle,  but  round  and  sharp 
enough  to  give  a  clear,  dark,  strong  line. 


INSTRUMENTS  AND  THEIR  USES  9 

5.  Pocket  Case  of  Drawing  Instruments.  It  is  a  common 
belief  among  students  that  any  kind  of  cheap  instrument 
will  do  with  which  to  learn  mechanical  drawing,  and  not 
until  they  have  acquired  the  proper  use  of  the  instruments 
should  they  spend  money  in  buying  a  first-class  set.  This 
is  one  of  the  greatest  mistakes  that  can  be  made.  Many  a 
student  has  been  discouraged  and  disgusted  because,  try  as 
he  would,  he  could  not  make  a  good  drawing,  using  a  set  of 
instruments  with  which  it  would  be  difficult  for  even  an 
experienced  draftsman  to  make  a  creditable  showing. 

If  it  is  necessary  to  economize  in  this  direction  it  is  better 
and  easier  to  get  along  with  a  fewer  number,  and  have  them 
of  the  best,  than  it  is  to  have  an  elaborate  outfit  of  ques- 
tionable quality. 


FIG.  12. 

The  instruments  shown  in  Fig.  12  are  well  made,  of  a 
moderate  price,  and  with  care  and  attention  will  give  good 
satisfaction  for  a  long  time. 

This  set  consists  of: 

i  large  compass,  with  pen  and  pencil  points  and  length- 
ening bar. 

i  large  divider,  sometimes  called  spacer. 

3  spring  bow  instruments  for  pen,  pencil  and  spacer. 


10  ,  MECHANICAL  DRAWING 

2  straight-line  drawing  pens,  medium  and  short  size. 

i  pencil  point  holder. 

i  compass  joint  tightener. 


FIG.  13. 

6.  The  large  compass  in  detail  is  shown  in  Fig.  13.  A  is 
the  needle  leg;  B,  the  pencil  leg;  C  the  pen,  and  D,  the 
lengthening  bar. 

This  instrument  is  used  for  drawing  arcs  and  circles  larger 
than  can  be  properly  drawn  with  the  spring  bows  (Fig.  19). 

Circles  of  about  3^"  diameter  may  be  drawn  with  the 
legs  straight.  See  Figs.  15  and  16. 


FIG.  14. 

The  method  of  operation  when  using  the  large  compass  is 
as  follows:  Adjust  the  needle  point  so  that  its  flat  side  is 
next  to  the  pencil  or  pen  and  its  point  about  -£%'  longer  than 
the  point  of  the  pencil  or  pen.  When  the  point,  through 
which  the  curve  is  to  be  drawn,  has  been  accurately  marked 
and  the  center  located,  guide  the  needle  point  to  the  center 


INSTRUMENTS  AND  THEIR  USES 


11 


with  the  little  finger  of  the  left  hand,  see  Fig.  14,  and  draw 
the  curve  exactly  through  the  mark  already  located  with  a 
clockwise  motion  inclining  the  instrument  a  little  toward  the 
direction  of  the  line,  see  Figs.  15  and  16,  which  illustrate  the 
beginning  and  ending  of  the  motion. 


FIG.  16. 


FIG.  15. 

When  circles  of  about  10"  diameter  are  to  be  drawn  the 
leg  of  the  compass  should  be  bent  at  the  knuckle  joints  so 
that  the  pencil  or  pen  leg  and  the  needle  leg  will  both  be 


FIG.  17. 

perpendicular  to    the   paper   to    provide   a   sharp   even   line 
throughout  its  length,  Fig.  17. 


12 


MECHANICAL  DRAWING 


Circles  larger  than  10"  diameter  up  to  about  14"  may  be 
drawn  with  the  use  of  the  lengthening  bar  shown  at  D  in 
Fig-  13- 


FIG.  i 8. 

/     :?V     ' 

To  use  the  lengthening  bar,  withdraw  the  pencil  qr  pen 
leg,  insert  the  bar,  add  the  pencil  or  pen  leg  and  bend  it 
and  the  needle  leg  at  the  knuckle  joint  and  the  instrument 
will  be  ready  for  use  as  shown  in  Fig.  18. 

7.  The  Spring  Bow  Instruments,  pen,  pencil  and  spacer, 
Fig.  19.  The  pencil  and  pen  bows  are  for  very  small  arcs 
and  circles,  such  as  joining  straight  lines  with  fillets,  etc. 


FIG.  19. 


INSTRUMENTS  AND  THEIR  USES  13 

These  are  very  important  instruments,  because  the 
beginner  by  their  use  is  able  to  make  a  uniformly  good  draw- 
ing. While  the  experienced  draftsman  may  put  in  small 
fillets  and  round  corners  free-hand,  he  can  take  this  liberty 
because  he  has  already  learned  the  use  of  the  spring  bows 
and  also  because  he  has  learned  to  do  such  freehand  work 
well,  but  the  beginner  has  no  such  experience  and  should, 
therefore,  practice  the  use  of  the  bow  instruments  at  every 
opportunity. 

Before  inking  or  tracing  a  drawing,  all  small  arcs,  such  as 
fillets  and  round  corners,  and  small  circles  should  be  care- 
fully pencilled  in  with  the  bow  instruments;  much  better 
work  is  obtained  than  is  probable  by  the  beginner  who, 
thinking  to  save  time  and  effort,  tries  to  ink  these  small 
curves  without  pencilling.  Many  otherwise  good  drawings  are 
spoiled  in  appearance  because  of  the  bad  joints  between 
curves  and  straight  lines. 

Small  arcs,  circles  and  all  curved  lines  of  any  description 
should  be  inked  in  all  over  the  drawing  before  any  straight 
lines  are  inked;  this  is  essential  to  obtain  the  best  results  in 
tracing  a  drawing. 

It  is  much  easier  to  know  where  to  stop  the  arc  line,  and 
to  draw  the  straight  line  tangent  to  it  than  it  is  to  reverse 
the  process. 


FIG.  20. 

8.  The  Large  Dividers  or  Spacers,  Fig.  20.  This  instru- 
ment should  be  held  in  the  same  manner  as  described  for  the 
compass.  It  is  very  useful  in  laying  off  equal  distances  on 
straight  lines  or  circles.  To  divide  a  given  line  into  any 
number  of  equal  parts  with  the  dividers,  say  12,  it  is  best 
to  divide  the  line  into  three  or  four  parts  first,  say  4,  and 
then  when  one  of  these  parts  has  been  subdivided  accu- 
rately into  three  equal  parts,  it  will  be  a  simple  matter  to 


14 


MECHANICAL  DRAWING 


step  off  these  latter  divisions  on  the  remaining  three-fourths 
of  the  given  line.  Care  should  be  taken  not  to  make  holes 
in  the  paper  with  the  spacers,  as  it  is  difficult  to  ink  over 
them  without  blotting. 

To  Divide  the  Line  by  Measurement.  First  ascertain  the 
length  of  the  given  line  by  measuring  with  rule  or  scale. 
Let  the  length  be  assumed  to  be  12"  and  the  line  is  to  be 
divided  into  12  equal  parts  as  before.  Such  divisicn  in  this 
case  will  equal  exactly  i" '.  Set  the  dividers  to  i"  on  the 
rule  or  scale  and  step  off  the  12  equal  parts  on  the  given 
line,  adjusting  the  dividers  until  the  line  is  divided  exactly 
into  the  required  number  of  equal  parts. 

9.  The  Straight-line  Pen,  Fig.  21.  There  are  usually 
two  pens  in  a  case  of  instruments,  one  about  5"  long  and  a 
smaller  one.  The  small  one  is  not  of  much  use.  The  theory 
is  that  the  small  pen  is  for  drawing  fine  lines  but  in  fact  the 
larger  pen  will  give  just  as  fine  lines  and  is  easier  to  handle. 


FIG.  21. 

The  best  form  for  a  straight-line  pen,  in  the  writer's 
opinion,  all  things  considered,  is  that  shown  in  Fig.  21. 
The  spring  on  the  upper  blade  spreads  the  blades  sufficiently 
apart  to  allow  for  thorough  cleaning  and  sharpening. 

The  pen  should  be  held  in  a  plane  passing  through  the 
edge  of  the  T-square  at  right  angles  to  the  plane  of  the 
paper,  and  making  an  angle  with  the  plane  of  the  paper 
ranging  from  60°  to  90°.  See  Fig.  22. 

The  blades  of  the  pen  should  be  of  equal  length  and 
when  held  against  the  T-square  or  triangle  with  the  blades 
parallel  to  their  edge,  the  pen  is  guided  by  the  upper  edge 
of  the  T-square  or  triangle  and  the  point  of  the  pen  is  held 
away  from  the  lower  edge  as  illustrated  at  B,  in  Fig.  23. 

Jf  the  pen  should  be  held  out  of  the  perpendicular,  as 


INSTRUMENTS  AND  THEIR  USES 


15 


shown  at  C,  the  result  would  probably  be  a  ragged,  uneven 
line;  if  held  as  shown  at  A,  there  is  danger  of  the  ink 
running  under  the  blade  of  the  straight  edge  and  causing  a 
blot. 


FRENCH 


B 


FIG.  23. 


10.  Sharpening  the  Pens.  The  best  of  drawing-pens  will 
in  time  wear  dull  on  the  point,  and  until  the  student  has 
learned  from  a  competent  teacher  how  to  sharpen  his  pens  it 
would  be  better  to  have  them  sharpened  by  the  manufac- 
turer. 

It  is  difficult  to  explain  the  method  of  sharpening  a  draw- 
ing-pen, 


16  MECHANICAL  DRAWING 

If  one  blade  has  worn  shorter  than  the  other,  the  blades 
should  be  brought  together  by  means  of  the  thumb-screw, 
and  placing  the  pen  in  an  upright  position  draw  the  point 
to  and  fro  on  the  oil-stone  in  a  plane  perpendicular  to  it, 
raising  and  lowering  the  handle  of  the  pen  at  the  same  time, 
to  give  the  proper  curve  to  the  point.  The  Arkansas  oil- 
stones are  best  for  this  purpose. 

The  blades  should  next  be  opened  slightly,  and  holding 
the  pen  in  the  right  hand  in  a  nearly  horizontal  position, 
place  the  lower  blade  on  the  stone  and  move  it  quickly  to 
and  fro,  slightly  turning  the  pen  with  the  fingers  and  ele- 
vating the  handle  a  little  at  .the  end  of  each  stroke.  Having 
ground  the  lower  blade  a  little,  turn  the  pen  completely  over 
and  grind  the  upper  blade  in  a  similar  manner  for  about  the 
same  length  of  time;  then  clean  the  blades  and  examine  the 
extreme  points,  and  if  there  are  still  bright  spots  to  be  seen 
continue  the  grinding  until  they  entirely  disappear,  and  finish 
the  sharpening  by  polishing  on  a  piece  of  smooth  leather. 

The  blades  should  not  be  too  sharp,  or  they  will  cut  the 
paper.  The  grinding  should  be  continued  only  as  long  as  the 
bright  spots  show  on  the  points  of  the  blades. 

ii.  The  Triangular  Scale,  Fig.  24.  This  scale,  illustrated 
in  Fig.  24,  was  arranged  to  su't  the  needs  of  the  students  in 
machine  drawing.  It  is  triangular  and  made  of  boxwood. 
The  six  edges  are  graduated  as  follows:  y^"  or  full  size, 
A",  r  and  r  =  i  ft,  i"  and  J"  =  i  ft,  3"  and  ij"  =  i  ic., 
and  4"  and  2"  =  i  ft. 

Drawings  of  very  small  objects  are  generally  shown  en- 
larged— e.g.,  if  it  is  determined  to  make  a  drawing  twice  the 
full  size  of  an  object,  then  where  the  object  measures  i"  the 
drawing  would  be  made  2",  etc. 

Larger  objects  or  small  machine  parts  are  often  drawn  full 
size — i.e.,  the  same  size  as  the  object  really  is— and  the  draw- 
ing is  said  to  be  made  to  the  scale  of  full  size,  or  12"  =  !  ft. 

Large  machines  and  large  details  are  usually  made  to  a 
reduced  scale — e.g.,  if  a  drawing  is  to  be  made  to  the  scale  of 
2//  =  i  ft.,  then  2"  measured  by  the  standard  rule  would  be 


INSTRUMENTS  AND  THEIR  USES 


17 


divided  into   12  equal    parts  and  each  part  would  represent 
i".     See  Fig.  24. 

When   laying   off   a   dimension   on   a   drawing   with   scale 


it  is  bad  form  to  use  the  compass  and  dig  the  needle  into 
the  scale  and  measure  the  dimension  with  the  instrument  on 
the  scale;  it  hurts  the  compass  and  mars  the  divisions  on 
the  scale.  The  best  way  is  to  lay  the  scale  on  the  drawing 


18 


MECHANICAL  DRAWING 


and  with  a  sharp-pointed    pencil   mark  the  distance  directly 
on  the  drawing.     See  Fig.  26. 


FIG.  26. 

To  lay  off  feet  and  inches,  see  Fig.  25. 

12.  The  Protractor,  Fig.  27.  This  instrument  is  for 
measuring  and  constructing  angles.  It  is  shown  in  Fig.  27. 
It  is  used  as  follows  when  measuring  an  angle:  Place  the 
lower  straight  edge  on  the  straight  line  which  forms  one  of 
the  sides  of  the  angle,  with  the  nick  exactly  on  the  point  of 
the  angle  to  be  measured.  Then  the  number  of  degrees 
contained  in  the  angle  may  be  read  from  the  left,  clock- 
wise. 


FIG.  27. 


In  constructing  an  angle,  place  the  nick  at  the  point  from 
which  it  is  desired  to  draw  the  angle,  and  on  the  outer  cir- 
cumference of  the  protractor,  find  the  figure  corresponding 


INSTRUMENTS  AND  THEIR  USES  19 

to  the  number  of  degrees  in  the  required  angle,  and  mark  a 
point  on  the  paper  as  close  as  possible  to  the  figure  on  the 
protractor;  after  removing  the  protractor,  draw  a  line  through 
this  point  to  the  nick,  which  will  give  the  required  angle. 

13.  The  Irregular  Curve  is  made  of  celluloid  and  should 
be  of  a  form  suitable  to  meet  most  needs  in  drawing  smooth 
irregular  lines.  The  Curve  shown  in  Fig.  28  is  useful  for 


FIG.  28. 

drawing  irregular  curves  through  points  that  have  already 
been  found  by  construction,  such  as  ellipses,  cycloids,  epicy- 
cloids, etc.,  as  in  the  cases  of  gear- teeth,  cam  outlines,  rotary 
pump  wheels,  etc. 

When  using  these  curves,  that  curve  should  be  selected 
that  will  coincide  with  the  greatest  number  of  points  on  the 
line  required. 

The  Curve  should  coincide  with  not  less  than  three  points 
at  each  drawing. 

14.  The  Emery  Pencil  Pointer,  Fig.  29.  The  lead  or 
graphite  in  the  pencil  must  not  be  cut  with  the  knife.  After 
the  wood  has  been  removed  the  lead  should  be  sharpened 


FIG.  29, 

on  the  Emery  Pencil  Pointer  in  the  manner  described  in 
Section  4  and  Figs.  9,  10,  and  n.  The  pointer  shown  in 
Fig.  29  is  the  best  style  for  handling  and  saves  the  soiling 
of  the  fingers. 

15.  The  Soft  Rubber  Eraser,  Fig.  30.     When  erasing  pen- 
cil lines,   the    rubber    should  not  be  pushed  hard  into   the 


20  MECHANICAL  DRAWING 

paper,  as  the  inclination  is,  but  hold  the  eraser  lightly  in  the 
fingers  and  try  to  erase  the  line  without  hurting  the  paper. 

When  removing  ink  lines  from  tracings  it  used  to  be 
thought  necessary  to  use  a  steel  or  glass  and  rubber  eraser, 
but  the  writer  found  this  to  be  unnecessary.  It  takes  an 
expert  to  use  a  steel  eraser  without  damaging  the  paper  and 
the  glass  rubber  will  always  leave  an  ugly  mark  which  will 
show  later  in  the  blue  print. 


(    - 


EMERALD 

E  BERNARD:  FALSER 

u. 


FIG.  30. 


To  erase  ink  lines  or  blots  from  tracings,  be  sure  the 
ink  is  perfectly  dry,  then  place  a  hard,  smooth  surface 
like  a  triangle  under  the  ink  to  be  erased  and  holding  the 
tracing  cloth  tightly  over  it  with  the  fingers  of  the  left 
hand  use  the  soft  rubber  with  short,  quick  strokes  and  rub 
off  the  ink,  not  in.  It  will  take  a  little  longer  to  make  the 
erasure  complete  than  it  would  using  the  steel  or  glass  rubber 
but  it  gives  much  better  results. 

When  pencil  or  ink  lines  are  to  be  erased  be  sure  to 
make  a  thorough  job  of  it.  If  the  erasing  is  not  complete 
it  will  always  have  a  bad  appearance. 

16.  An    erasing    shield    is    sometimes    used    to    take    out 
short   lines    and    spots.     The    idea    is    to    save    rubbing    the 
adjacent   lines    and   confine   the   rubbing   to    the   ink   to   be 
erased.     It  is   the   opinion   of   the   writer,   however,   that  an 
erasing  shield  is  unnecessary,  in  fact  may  be  a  detriment  to 
obtaining  good   results.     When  using  the  shield  the  rubbing 
is  confined   to  a  small  area  and  the  inclination  is  to  press 
hard    while    rubbing    with     consequent     danger    of    rubbing 
through  the  paper.  . 

17.  The   "  Art-gum,"   Fig.  31,  is  a  soft  material  used  for 
cleaning  the  drawing  after  all  the  inking  is  done.     It  takes 
the  place  of  and  is  better  than  sponge  rubber. 


INSTRUMENTS  AND  THEIR  USES  21 

Most  of  the  cleaning  should  be  done  before  inking. 
Gasoline  is  good  for  cleaning  tracings. 

Black  India  Ink,  Fig.  32,  is  a  liquid  waterproof  Chinese 
ink.  It  should  be  fresh  to  obtain  the  best  results. 

If  the  ink  has  become  thickened  in  hot  weather  it  may 
be  thinned  by  adding  a  few  drops  of  water.  Old,  stale, 
gritty  ink  will  give  trouble. 

Thumb  Tacks  for  fastening  the  drawing  paper  to  the 
board  are  made  of  stamped  steel.  Heads  of  f"  diameter 
are  large  enough.  Lines  should  not  be  drawn  with  the  T-- 
square resting  on  thumb  tacks.  Remove  the  tacks  tem- 
porarily so  that  the  T-square  may  lie  fiat  on  the  paper. 


FIG.  31.  FIG.  32.  FIG.  33. 

Thumb  tacks  come  one  dozen  in  a  small  box  like  that  shown 
in  Fig.  33. 

18.  Cross-section  Pad.  This  pad  is  8"Xio"  in  size  and 
is  divided  8X8  to  the  inch.  It  is  useful  in  making  the  eight 
sheets  of  lettering  included  in  this  course. 

It  is  also  used  in  machine  sketching,  taking  notes,  figuring 
calculations  in  determining  machine  proportions,  etc. 

Drawing  Paper.  Use  cream  detail  paper  i5"X2o".  This 
paper  is  cut  exactly  to  size  so  there  will  be  no  margin  to 
cut  off.  A  border  line  is  to  be  drawn  as  follows:  if"  from 
left-hand  edge  of  paper  and  \"  from  all  the  other  edges. 

Tracing  Cloth.  This  should  be  of  the  grade  called  "  Im- 
perial." Always  use  the  dull  side  of  the  tracing  cloth.  See 
the  answers  to  Question  31  in  "  Present  Practice  in  Drafting 
Room  Conventions,"  in  Appendix,  page  225. 


CHAPTER  H 

STANDARD  DRAFTING  ROOM  CONVENTIONS 

19.  In  most  drafting   rooms,   each   draftsman   is  supplied 
with    a    set   of    conventions,    rules    of   procedure    in    making 
working  drawings,  etc. 

Endeavors  have  been  made,  from  time  to  time,  with  a 
large  measure  of  success,  to  establish  uniform  conventions, 
rules  and  methods  in  making  commercial  drawings. 

The  importance  of  a  uniform  system  is  apparent  when  we 
realize  that  shopmen  have  often  to  use  drawings  made  by 
the  draftsmen  of  different  companies. 

The  following  rules  and  conventions  adopted  for  this 
work  have  been  found  by  investigation  to  be  of  nearly  uni- 
versal practice  in  all  the  leading  and  progressive  drafting 
rooms  in  the  United  States. 

20.  Pencil  Drawings.     Unless  otherwise  ordered  all  pencil 
drawings   shall  be  made  on  cream   detail  paper  with  a  6H 
pencil  sharpened  as  directed  in  Section  4.     This  applies  to 
both  straight-line  and  compass  pencil. 

Pencil  diawings  are  to  be  finished  and  all  lettering,  figures 
and  arrow  points  made  with  the  4H  pencil,  sharpened  to  a 
conical  point. 

On  all  pencil  drawings  the  title,  bill  of  material  and  border 
lines  are  to  be  inked. 

21.  Tracings  are  to  be  made  on  the  dull  side  (see  answer 
to   Question  31,  page  225  in  Appendix)  of  "  Imperial  "  tracing 
cloth.     When   erasing   is   necessary   use    "  Emerald "    rubber 
and  triangle. 

Soiled  tracings  can  be  cleaned  with  gasoline  or  benzine. 

22.  Lettering.     The  lettering  on  all  drawings  shall  be  free- 

22 


STANDARD  DRAFTING  ROOM  CONVENTIONS 


23 


hand,  sloping,  Gothic  capitals,  of  uniform  height.  (See 
answer  to  Question  8  in  Appendix.)  All  notes  on  drawings 
are  to  be  A"  high.  The  size  of  figures  in  dimensions  may 
vary  according  to  conditions.  The  dividing  line  in  fractions 
must  always  be  made  horizontal. 

23.  Bill  of  Material.  When  a  bill  of  material  is  given  on 
an  Elementary  Machine  Drawing  it  should  conform  in  every 
respect  to  that  shown  in  Fig.  34. 


MO.MTL. 


REMARKS. 


Hr 


FIG.  34. 

The  letters  in  the  words  "  Bill  of  Material  "  are  to  be 
inked  with  heavy  lines  as  shown. 

The  "  Ball  "  point  pen  No.  516  is  to  be  used  for  all  letters 
and  figures. 

The  extra  width  of  lines  in  letters  that  are  to  be  made 
heavy  should  be  applied  with  the  "  Gillott  "  pen  No.  303  to 
insure  a  sharp  even  outline. 

The  lowest  line  in  the  table  of  the  bill  of  material  should 
be  drawn  |"  above  the  highest  line  of  the  title. 

The  outer  boundary  lines  and  the  line  under  the  words 
"  Bill  of  Material  "  are  to  be  inked  with  heavy  lines  as 
shown  in  Fig.  34. 

24.  Standard  Title.  All  drawings  in  mechanical  and  ma- 
chine drawing  shall  have  a  title  conforming  to  the  standard 
title  shown  in  Fig.  35. 

The  title  will  occupy  a  space  of  about  2//X4^'/  and  be 
placed  at  the  lower  right-hand  corner  of  the  plate  ^"  inside 
of  the  border  line. 

There  shall  be  no  boundary  line  drawn  around  the  title. 

The  guide  lines  for  the  lettering  in  the  title  and  bill  of 


24  MECHANICAL  DRAWING 

material      should    be    drawn    very    narrow    and    light    and 
erased  as  far  as  possible  before  inking  the  lettering. 

^       .. 


>*a     .  i        —GEOMETmGML- 


NOP       ^  \       ^FFVL.  tlCS,  /Mtt.  Crt/G4G&,  /LL. 


FIG.  35- 

25.  Standard  Lines. 

Visible  Object  Lines 

Visible  object  lines  in  ink  on  tracings  shall  be  not  less 
than  sV',  nor  more  than  A",  wide. 

A  ————————  Visible  object  line  TO" 

Invisible  Object  Lines 

B         ' "^^ '         '         '         ^^3 1         '_         IZZI  Invisible  object  lines  TB  " 

Invisible  object  lines  in  ink  shall  be  about  T^"  wide.  The 
dashes  are  to  be  not  less  than  J"  nor  more  than  3^"  in  length, 
J"  for  short  dash  lines  and  iV  f°r  l°ng  dash  lines. 

The  spaces  between  dash  lines  are  to  be  very  short,  just 
enough  to  show  that  the  line  is  broken. 

When  two  invisible  object  lines  have  to  be  drawn  close 
together,  as  shown  at  B,  the  breaks  should  be  evenly  ar- 
ranged under  one  another.  It  is  a  much  neater  arrangement 
than  that  shown  at  C. 

C  Z  ~  Incorrect  arrangement 


STANDARD  DRAFTING  ROOM  CONVENTIONS  25 


Center  Line 

Center  lines  shall  have  a  long  dash  and  a  short  one 
alternately.  In  a  long  center  line  the  long  dash  may  be  3" 
long  and  the  short  dash  f"  and  the  spaces  between  them 
-£2"  '.  In  short  center  lines  the  long  dash  may  be  made  to 
suit  but  the  short  dash  should  always  be  about  f"  long. 
See  D. 


D    -  ----------  Center  line 

The  center  line  must  be  made  very  narrow.  If  the  pen 
is  worn  so  that  it  will  not  make  a  narrow  line  stop  using  it 
until  it  is  sharpened. 


Dimension  Line 

—  --  *_^.  Dimension  line 


Dimension  lines,  as  shown  at  E,  are  to  be  very  narrow 
with  a  suitable  break  for  the  dimension  and  usually  an  arrow 
point  at  each  end. 

Arrow  points  should  be  sharp  at  point  and  narrow  at  the 
wings.  Radial  dimension  lines  drawn  from  a  center  should 
have  no  arrow  point  at  the  center. 

Witness   Line 
•^•T  "  -  Witness  line 


Witness  lines  are  short  lines  extending  from  any  part  of 
a  drawing  to  meet  the  dimension  line  outside  of  the  part 
to  be  dimensioned.  Witness  lines  must  be  very  narrow;  it  is 
a  broken  line,  one  short  dash  about  f  "  long,  one  break  and 
another  longer  dash  to  pass  the  arrow  point  on  the  dimen- 
sion line  about  jV'.  The  dimension  line  should  be  far 
enough  away  from  the  part  to  be  dimensioned  to  give  plenty 
of  room  for  the  dimension  figures  without  crowding. 


26  MECHANICAL  DRAWING 

Dimension  figures  should  not  be  placed  close  to  lines  or 
other  figures.  Dimensions  may  be  placed  upon  the  drawing, 
sometimes  with  good  effect,  but  a  good  general  rule  is  to 
place  all  dimensions  outside  of  a  piece  whenever  it  is  con- 
venient to  do  so. 


Limiting  Break  Line 

^—~~~——-—*~~~—  Limiting  break  line 


When  only  a  small  portion  of  an  object  needs  to  be 
shown  it  should  be  limited  by  drawing  a  break  line,  as  above, 
freehand,  with  a  lettering  pen.  The  line  should  not  be  very 
ragged,  just  waved  enough  to  show  the  character  of  the  line. 

Adjacent  Part  Line 

Adjacent  part  lines  are  sometimes  shown  to  indicate  a 
part  connected  with  that  for  which  the  drawing  is  made  but 
is  not  an  essential  part  of  that  drawing. 

The  line  is  made  with  J"  dashes  of  medium  weight  and 
short  spaces.  See  Fig.  115,  which  illustrates  the  use  of  an 
adjacent  part  line. 

Alternate  Position  Line 

Alternate  position  line 


An  alternate  position  line  is  used  to  represent  a  limit 
position  of  a  moving  part.  The  base  outline  of  the  object 
may  be  shown  at  one  or  more  of  its  extreme  positions,  while 
the  regular  drawing  shows  it  at  its  central  position.  The 
line  is  made  of  fine  dashes  f  "  and  J"  long,  alternately.  The 
space  between  the  dashes  should  be  quite  short.  The  alter- 
nate positions  of  the  crosshead  on  an  engine  is  an  example. 


STANDARD  DRAFTING  ROOM  CONVENTIONS 


27 


Cutting  Plane  Line 


Cutting  plane  line 


A  cutting  plane  line  is  used  to  indicate  on  a  drawing 
where  a  sectional  view  is  to  be  taken  other  than  on  a  center 
line.  The  character  of  the  line,  as  shown  above,  is  com- 
posed of  dashes  f"  long  divided  by  two  short  dashes  about 
yV"  long  each.  The  spaces  between  all  the  dashes  to  be 
very  short.  The  dashes  are  to  be  of  medium  width,  say 
about  sV". 

BORDER  LINES: 

REFERENCE  ARROW 

LINES 

Should  always  be  drawn  straight 
with  ruling  pen  and  set  obliquely, 
i.e.,  neither  vertically  nor  hori- 
zontally. 

Hatch  Lines 


Hatch  lines  are  used  to  indicate  parts  of  a  drawing  in 
section.  They  are  sometimes  called  section  lines.  They 
should  be  drawn  TV"  apart  at  an  angle  of  45°. 

When  two  adjacent  surfaces  in  section  are  to  be  hatch- 
lined  the  hatch  lines  on  the  two  surfaces  should  be  drawn  in 
opposite  directions.  When  three  or  more  surfaces  of  different 
objects  come  together  in  a  section  drawing  the  hatch  lines 
must  be  drawn  at  two  different  angles  and  two  opposite 
directions. 

26.  Standard  Hatch  Lines.  Conventional  hatch  lines  are 
placed  on  drawings  to  distinguish  the  different  kinds  of 
materials  used  when  such  drawings  are  to  be  finished  in 
pencil  or  traced  for  blue  printing,  or  to  be  used  for  a  repro- 
duction of  any  kind. 

Fig.  36  shows  a  collection  of  hatch-lined  sections  that 
is  now  the  almost  universal  practice  among  draftsmen  in 
this  and  other  countries,  and  may  be  considered  standard. 


28 


MECHANICAL  DRAWING 


STANDARD  DRAFTING  ROOM  CONVENTIONS 


29 


Conventional  Breaks 

27.  Conventional  Breaks.  Breaks  are  used  in  drawings 
sometimes  to  indicate  that  the  thing  is  actually  longer  than 
it  is  drawn,  sometimes  to  show  the  shape  of  the  cross-section 
and  the  kind  of  material.  Those  given  in  Fig.  37  show  the 
usual  practice. 


FIG.  37- 


28.  Finishes. 


Finish,    f. 

Shape  to  dimensions  with  a  cutting  tool:  The  surface  to 
conform  to  good  shop  practice.  Finish  for  appearance  sake 
only  when  so  specified. 

Trim 

Shape  by  any  convenient  method  such  as  chipping,  filing, 
grinding,  etc. 

Spot  Face 
Use  counterbore  or  similar  tool  to  make  the  spot  true. 

Polish 

Make  the  surface  smooth  and  glossy  when  used  without 
connection  with  the  word  "  finish  "  or  the  finish  mark  "  f  "; 


30  MECHANICAL  DRAWING 

neither  a  perfectly  true  surface  nor  measured  adherence  to 
dimensions  is  called  for.  A  suitable  polish  may  be  had 
by  first  grinding  and  then  buffing. 

Finish  and  Polish 

Shape  to  dimensions  with  a  cutting  tool  and  make  the 
surface  smooth  and  glossy  without  destroying  the  accuracy 
of  the  work. 

Grain 

Give  the  surface  the  appearance  of  having  a  straight  grain, 
by  rubbing  with  emery  cloth  in  a  direction  parallel  with  one 
of  the  edges  of  the  surface. 

Finish  and  Grain 

Shape  to  dimensions  with  a  cutting  tool  and  afterwards 
increase  the  trueness  of  the  surface  by  scraping. 

Finish  and  Grind 

Shape  to  dimensions  with  a  cutting  tool  and  afterwards 
increase  the  trueness  of  the  surface  by  grinding. 

Matt 

Cover  uniformly  with  indentations,  touching  one  another 
and  all  of  the  same  size,  shape  and  depth. 

Blue 
Heat  uniformly  until  the  color  changes  to  blue. 

Nickel   Plate 
Electroplate  with  nickel. 

Lacquer  Blue 
Coat  with  blue  lacquer, 


STANDARD  DRAFTING  ROOM  CONVENTIONS  31 

Dip  and  Lacquer 

Cleanse  by  immersing  in  acid,  afterwards  coat  with  yellow 
lacquer. 

Boil  in  Oil 
Immerse  in  boiling  linseed  oil. 

Burn  in  Oil 

Heat  to  dull  red  and  plunge  into  linseed  oil.      Or  dip  cold 
into  linseed  oil  and  afterwards  burn  the  oil  off. 

French  Polish 

Coat  with  shellac  and  boiled  linseed  oil  by  the    process 
known  as  French  polishing. 

Shellac 
Coat  with  a  suitable  thickness  of  shellac. 

Black  Japan 

Bake    upon    the    surface    a    suitable    thickness     of    black 
enamel  paint. 

Dip  in  Linseed  Oil 
Immerse  in  boiled  linseed  oil. 

Paraffin 
Immerse  in  boiling  paraffin. 

Sand  Rub  and  Oil 

Rub  with  sandstone,  wipe  clean  and  apply  boiled  linseed 
oil. 

Paint 
Coat  with  a  suitable  thickness  of  paint. 


32  MECHANICAL  DRAWING 

Knurl 

Using    a    knurling  tool  make    the    surface    suitable    for 
gripping.     There  are  two  standard   styles  of  ^ 

knurling.  «((((() ))))))» 

1.  Straight  knurl  for  round  edge  grips   A 
not  to  exceed  J". 

2.  Diamond  knurl,  standard  medium. 

Pene 

Close  the  fibers  of  the  material  or  produce  closer  contact 
between  pieces  by  hammering. 

Designate  finishes  on  drawings  as  follows: 

Finish 

In  general  indicate  by  applying  /  on  the     ^ 

edge  line  of  the  surface  to  be  finished  thus: 
When  a  surface  is  of  such  shape  as  to  require  several  finish 
marks  inconveniently  close  together 
the  finish  may  be  indicated   thus: 
This   means   that  the   entire   sur- 
face between  the  arrow  points  is  to  be  finished.     If  desired  an 
explanatory  note  may  be  used  as  "  Finish  all  over  "  using  the 
complete  word  finish. 

Trim 

Indicate  by  an  explanatory  note  as  "  trim  flush  with  edge 
of  flange  "  using  the  complete  word  trim. 

Spot  Face 
Indicate  thus:   "  Spot  face." 

Polish 

Indicate  by  note,   as  "  Polish  exposed  surfaces,"  or  thus: 

*_         polish When  desirable  indicate  thus:   "  Finish 

~~1     and  Polish  from  A  to  B," 


STANDARD  DRAFTING  ROOM  CONVENTIONS  33 


Finish  Smooth 

In  general  indicate  thus:         ^  _  Smooth 
or  thus  :  Finish  smooth  from    —  ' 
A  to  B. 

Finish  and.  Scrape 

s  _  Scrape  _ 


,—  ,, 

Thus  : 


Thus: 


Thus: 


Finish  and  Grind 

Grind 

Finish  and  Grain 

Grain 


or  "  Face  and  grain  exposed  surfaces." 

Matt 
Thus:       ~1 


Nickel  Plate 
Indicate  by  note  using  abbreviation  "  N.P." 

All  other  finishes 

As  Blue,  Copper  Plate,  Copper  Plate  and  oxidize,  Lacquer, 
Boil  in  Oil,  French  Polish,  Shellac,  Black  Japan,  Dip  in  Linseed 
Oil,  Paraffin,  Sand  Rub  and  Oil,  and  Paint  indicate  by  note 
in  Gothic  letters  &"  high. 

29.  Abbreviations.     Abbreviations    are    useful    in    saving 
time  and  space.      Most  of  the  abbreviations  given  here  are 
common    and    well    known.       The    meaning    of    uncommon 
abbreviations    is    suggested    by    preceding   words    or    by   the 
drawing. 
Alternating  current  .  ...................  A.C. 

Amperes  ..............................  Amp. 

Aluminum.  .  .  .  Almn. 


34  MECHANICAL  DRAWING 

Babbitt Bb. 

Back  gear BGr. 

Bevel  gear Bev.Gr. 

Birmingham  wire  gauge B.W.G. 

Board Bd. 

Bolt • B. 

Bracket Bkt. 

Brass Br. 

Bronze Brz. 

Building Bldg. 

Button  head  bolt Btn.Hd.Bc 

Cabinet Cab. 

Candle  power C.P. 

Cap  screw Cap.Sc. 

Carriage Car. 

Case  harden C.H. 

Cast  brass C.B. 

Cast  copper C.Cop. 

Cast  iron C.I. 

Cast  steel C.S. 

Center  line C. 

Center Ctr. 

Change  gear Ch.Gr. 

Circular  pitch C.P. 

Cold-rolled  steel C.R.S. 

Company Co. 

Compound  rest Comp.R, 

Conical A 

Counterbore C.br. 

Countersink Csk. 

Counter  shaft Co.Sh. 

Centimeter Cm. 

Circumference Circume 

Corona  steel Cro.S. 

Crank Cr. 

Crucible  steel Cru.S. 

Cylinder Cyl. 


STANDARD  DRAFTING  ROOM  CONVENTIONS  35 

Degrees  Centigrade 15°  C. 

Degrees  Fahrenheit 15°  F. 

Department Dept. 

Diameter Dia. 

Diametral  pitch D.P. 

Direct  current D.C. 

Double  back  gear D.B.Gr. 

Double  bevel  gear D.Bev.Gr. 

Double  chamfered  hexagon  nut Dbl.Chmfd.Hex.Nuk 

Drawing Dwg. 

Drill Dl. 

Electrical Elect. 

Electromotive  force E.M.F. 

Experiment Exp. 

Eye  bolt EyeB. 

Feather Fthr. 

Feet  or  foot Ft. 

Feet  or  foot  and  inches 2 Y' 

Fillister  head  brass  machine  screw Fil.Hd.B.M.Sc. 

Fillister  head  iron  machine  screw Fil.Hd.LM.Sc. 

Finish f. 

Flat  head  stove  bolt Fl.H.StoveB. 

Flat  head  wood  screw Fl.H.Wd.Sc. 

Flexible Flex. 

Force  or  weight F.f . 

General Gnl. 

Half  nut H.N. 

Hand  wheel H.W. 

Hardened H. 

Head Hd. 

Head  stock Hd.St. 

Headless  set  screw Hdlss.Set  Sc. 

Hexagon Hex. 

Hexagon  nut Hex.Nut. 

Horsepower H.P. 

Inch  or  inches - In.,  Ins.  or  " 

Kilowatts..  ..K.W. 


36  MECHANICAL  DRAWING 

Kilogram Kg. 

Kilometer vKm. 

Lag  screw Lag  Sc. 

Lead Lead. 

Lead  screw L.Sc. 

Length L.  or  1. 

Long Lg. 

Lower  side .  .L.S1. 

Machine Mach. 

Machine  screw M.Sc. 

Machinery  steel M.S. 

Malleable  iron Mai. I. 

Manufacturing Mfg. 

Material Mtl. 

Maximum Max. 

Medium  steel Med.S. 

Metres M. 

Mild  steel St. 

Milled  body  tap  bolt M.B.Tap  B, 

Millimeters mm. 

Minimum Min. 

Moment  of  inertia K. 

Negative Neg. 

Not  to  scale N.T.S. 

Nickel  plate N.P. 

Number  for  designating No.  or  $  . 

Number :  quantity Nbr. 

Octagonal Oct. 

Open-hearth  steel O.H.S. 

Oval 0. 

Ounce  or  ounces Oz. 

Pattern  number Patt.  #  . 

Percent % 

Pieces PCS. 

Pitch Pi. 

Pitch  diameter • P.D. 

Phosphor Ph. 


STANDARD  DRAFTING  ROOM  CONVENTIONS  37 

Phosphor  brcnze Ph.Brz. 

Polish Pol. 

Positive Pos. 

Power P. 

Power  feed P.F. 

Pressure p. 

Quadrant Quad. 

Radius R.  or  Rad. 

Railway Ry . 

Ream . Rm. 

Revolutions  per  minute R.P.M. 

Rough R. 

Screw .  Sc. 

Seamless Smlss. 

Set  screw Set  Sc. 

Shaft Sh. 

Shoulder  screw Sh.Sc. 

Sketch Sk. 

Specification Spec. 

Square Sq. 

Square  feet . .  n' 

Square  inch Q" 

Standard Std. 

Stationary  part Stator. 

Steel S. 

Steel  castings S.C. 

Stud  bolt Stud  B. 

T-head  bolt T.Hd.B. 

Tap Tp. 

Temperature Temp. 

Threads .  .Thds. 

Tool  steel T.S. 

Weight Wgt. 

Wrought  iron W.I. 

30.  Geometrical  Definitions.  To  those  who  have  studied 
geometry  the  following  definitions  will  simply  be  reminders  of 
things  learned  and  partially  forgotten. 


38  MECHANICAL  DRAWING 

There  are,  however,  some  who  have  never  studied  geometry 
who  believe  that  mechanical  drawing  would  be  a  great  assistance 
to  them  in  their  work.  They  are  right,  there  is  no  subject  of 
such  a  practical  nature  known  to  the  writer  that  can  be  so  easily 
acquired  and  at  such  little  cost  of  time,  labor  and  money  as 
mechanical  drawing  and  be  of  such  a  benefit  to  them,  no  matter 
what  their  business  may  be  in  this  age  of  practical  engineering. 
A  practical  knowledge  of  mechanical  drawing  can  be  acquired 
without  a  previous  study  of  geometry.  The  following  definitions 
will  be  illuminating  and  interesting  to  those  taking  up  mechanical 
drawing  before  having  studied  geometry. 

1.  Geometry  is  the  science  of  space,  whether  linear,  super- 
ficial or  solid.     It  treats  of  points,  lines,  surfaces  and  solids,  their 
construction  and  measurement. 

2.  A  Point  has  position  but  neither  length,  breadth  nor 
thickness. 

3.  A  Line  has  length  but  no  breadth  or  thickness. 

4.  A  Straight  Line  or  Right  Line  is  the  shortest  distance 
between  two  points. 

5.  A  Curved  Line  is  a  line  no  part  of  which  is  straight. 

6.  Parallel  Lines  are  equidistant  from  each  other  in  the  same 
plane  and  never  meet  however  far  they  may  be  produced. 

7.  A  Horizontal  Line  is  a  line  parallel  to  the  horizon.     A 
horizontal  line  in  a  drawing  is  usually  drawn  with  the  T-square 
from  left  to  right. 

8.  A  Vertical  Line  is  a  line  that  is  perpendicular  to  the  plane 
of  the  horizon.     A  still  plumb  line  is  a  vertical. 

In  a  drawing  a  vertical  may  be  drawn  up  and  down  the  paper 
with  T-square  and  right-angled  triangle. 

9.  Oblique  Lines  are  neither  horizontal  nor  vertical  but  are 
inclined  to  both. 

10.  Perpendicular  Lines.    A  line  is  perpendicular  to  another 
line  when   the   angles   on   either    side   of    it    form   two  right 
angles. 

Vertical  and  horizontal  lines  are  always  perpendicular  to 
each  other  but  all  perpendicular  lines  are  not  horizontal  and 
vertical. 


STANDARD  DRAFTING  ROOM  CONVENTIONS  39 

11.  A  Plane  is  a  surface  such  that  if  any  two  of  its  points  be 
joined  by  a  straight  line  that  line  will  lie  wholly  in  that  surface. 
A  surface  has  length  and  breadth  without  thickness. 

12.  A  Plane  Figure  is  a  portion  of  a  plane  bounded  on  all 
sides  by  straight  or  curved  lines. 

13.  A  Plane  Figure  bounded  by  straight  lines  is  a  rectilinear 
figure. 

14.  An   Angle.     Two   straight   lines   which   intersect   each 
other  form  an  angle.     The  point  of  intersection  is  called  the 
Vertex  of  the  angle. 

15.  A  Right  Angle  is  formed  when  two  straight  lines  meet  and 
are  perpendicular  to  each  other. 

1 6.  An  Acute  Angle  is  less  than  a  right  angle. 

17.  An  Obtuse  Angle  is  greater  than  a  right  angle. 

1 8.  A  Triangle  is  a  plane  surface  bounded  by  three  straight 
lines. 

19.  An  Equilateral  Triangle  has  all  of  its  sides  equal. 

20.  An  Isosceles  Triangle  has  two  sides  equal. 

21.  A  Scalene  Triangle  has  all  of  its  three  sides  unequal. 

22.  A  Right-angled  Triangle  has  one  of  its  angles  a  right 
angle. 

23.  An  Acute-angled  Triangle  has  three  acute  angles. 

24.  An  Obtuse-angled  Triangle  has  one  obtuse  angle. 

25.  The  Apex  of  a  Triangle  is  the  upper  extremity.     Some- 
times called  the  vertex. 

26.  The   Hypothenuse  is  the  longest  side  of  a  right-angled 
triangle.     It  is  opposite  the  right  angle. 

27.  The  Base  is  the  bottom  side  of  a  triangle. 

28.  The  Vertex  is  the  point  in  any  figure  opposite  to  and 
furthest  from  the  base. 

29.  The  Altitude  of  a  triangle  is  the  length  of  a  perpendicular 
from  the  apex  to  the  base. 

30.  A  Quadrangle  or  Quadrilateral  is  a  figure  of  four  sides  and 
has  particular  designations  as  follows: 

Parallelogram,  having  its  opposite  sides  parallel. 
Square,  having  length  and  breadth  equal. 
Rectangle,  all  its  angles  are  right  angles. 


40  MECHANICAL  DRAWING 

Rhombus  or  Lozenge  has  equal  sides  but  its  angles  are  not 
right  angles. 

Rhomboid  has  only  its  opposite  sides  equal.  Its  angles  are 
not  right  angles. 

Trapezium,  has  unequal  sides. 

Trapezoid,  only  one  pair  of  opposite  sides  are  parallel. 

Gnomon.  The  space  included  between  the  lines  forming  two 
parallelograms,  of  which  the  smaller  is  inscribed  within  the  larger 
so  as  to  have  one  angle  in  each  common  to  both. 

31.  Polygons  are  plane  figures  having  more  than  four  sides 
and  are  either  regular  or  irregular  according  as  their  sides  and 
angles  are  equal  or  unequal.     They  are  named  from  the  number 
of  their  sides  or  angles,  thus: 

Pentagon,  five  sides  Ocatgon,  eight  sides  Undecagon,  eleven  sides 

Hexagon,  six  sides  Nonagon,  nine  sides  Dodecagon,  twelve  sides. 

Heptagon,  seven  sides  Decagon,  ten  sides 

32.  A  Circle  is  a  plane  figure  bounded  by  a  curved  line 
every  point  of  which  is  equidistant  from  the  center. 

33.  A  Diameter  is  a  right  line  passing  through  the  center  of  a 
circle  or  a  sphere  and  terminated  at  each  end  by  the  periphery 
or  surface. 

34.  An  Arc  is  any  part  of  the  circumference  of  a  circle. 

35.  A  Chord  is  a  right  line  joining  the  ends  of  an  arc. 

36.  A  Segment  of  a  circle  is  any  part  of  a  circle  bounded  by 
an  arc  and  its  chord. 

37.  A  Radius  of  a  circle  is  a  line  drawn  from  its  center  to 
circumference. 

38.  A  Sector  is  any  part  of  a  circle  bounded  by  an  arc  and  its 
two  radii. 

39.  A  Semicircle  is  half  a  circle. 

40.  A  Quadrant  is  a  quarter  of  a  circle. 

41.  A  Zone  is  a  part  of  a  circle  included  between  two  parallel 
chords. 

42.  A  Lune  is  the  space  between  the  intersecting  arcs  of  two 
eccentric  circles. 

43.  A  Secant  is  a  line  running  from  center  of  circle  to  extremity 
of  tangent  of  arc. 


STANDARD  DRAFTING  ROOM  CONVENTIONS  41 

44.  Cosecant  is  secant  of  complement  of  an  arc,  or  line  run- 
ning from  center  of  circle  to  extremity  of  co- tangent  of  arc. 

45.  Sine  of  an  arc  is  a  line  running  from  one  extremity  of  an 
arc   perpendicular   to   a   diameter  passing   through   the   other 
extremity,  and  sine  or  angle  is  sign  of  arc  that  measures  that 
angle. 

46.  Versed  Sine  of  an  arc  or  angle  is  part  of  diameter  inter- 
cepted between  sine  and  arc. 

47.  Cosine  of  an  arc  or  angle  is  part  of  diameter  intercepted 
between  sine  and  center. 

48.  Coversed  Sine  of  an  arc  or  angle  is  part  of  secondary 
radius  intercepted  between  cosine  and  circumference. 

49.  Tangent  is  a  right  line  that  touches  a  circle  without  cut- 
ting it. 

50.  Cotangent  is  tangent  of  complement  of  arc. 

51.  Circumference  of  every  circle  is  supposed  to  be  divided 
into  360  equal  parts  termed  Degrees;  each  degree  into  60  minutes 
and  each  minute  in  60  seconds. 

52.  Complement  of  an  angle  is  what  remains  after  subtracting 
angle  from  90°. 

53.  Supplement  of  an  angle  is  what  remains  after  subtracting 
angle  from  180°. 

54.  Vertex  in  Conic  Sections  is  the  point  through  which  the 
generating  line  of  the  conical  surface  always  passes. 

55.  Measure  of  an  angle  is  an  arc  of  a  circle  contained  between 
the  two  lines  that  form  the  angle  and  is  estimated  by  number  of 
degrees  in  arc. 

56.  Segment  is  a  part  cut  off  by  a  plane  parallel  to  the  base. 

57.  Frustum  is  part  remaining  after  segment  is  cut  off. 

58.  Perimeter  of  a  figure  is  the  sum  of  all  its  sides. 

59.  Circular  Cylinder.     A  figure  formed  by  revolution  of  a 
right-angled  parallelogram  around  one  of  its  sides. 

60.  Prism.    A  figure  whose  sides  are  parallelograms  and  ends 
equal  and  parallel. 

61.  Wedge,  a  prolate  triangular  prism. 

62.  A  Triangular  Prism  has  triangular  bases. 

63.  A  Quadrangular  Prism  has  quadrilateral  bases. 


42  MECHANICAL  DRAWING 

64.  A  Pentagonal  Prism  is  one  whose  bases  or  ends  are  pen- 
tagons. 

65.  A  Hexagonal  Prism  has  hexagons  for  bases. 

66.  A  Cube  is  a  prism  whose  six  faces  are  all  squares. 

67.  An  Elliptical  Cylinder  is  one  whose  bases  are  ellipses. 

68.  An  Oblique  Cylinder  is  one  whose  curved  surface  is  in- 
clined to  its  bases. 

69.  A  Cone  is  a  round  solid  with  a  circle  for  its  base,  and 
tapering  uniformly  to  a  point  at  the  top  called  the  apex. 

70.  A  Right  Cone  is  one  in  which  the  perpendicular  from  the 
apex  passes  through  the  center  of  the  base.     This  perpendicular 
is  called  the  axis  of  the  cone. 

71.  An  Oblique  or  Scalene  Cone  has  its  axis  inclined  to  the 
plane,  of  its  base. 

72.  A  Truncated  Cone  is  one  whose  upper  part  is  cut  off  by 
a  plane  parallel  to  its  base. 

73.  A  Pyramid  is  a  solid  with  a  straight-sided  base  and  tri- 
angular sides  terminating  in  the  apex.     Pyramids  are  named  by 
the  forms  of  their  bases  as  triangular,  quadrangular,  pentagonal, 
hexagonal,  septagonal,  etc. 

74.  A  Right  Pyramid  has  a  regular  polygon  for  a  base  and 
its  axis  is  perpendicular  to  and  passes  through  the  center  of  the 
base. 

75.  A  Polyhedron  is  a  solid  bounded  by  plane  figures. 

76.  A  Tetrahedron  is  bounded  by  four  equilateral  triangles. 

77.  Hexahedron  is  bounded  by  six  squares,  a  cube. 

78.  Octrahedron  is  bounded  by  eight  equilateral  triangles. 

79.  Dodecahedron  is  bounded  by  12  pentagons. 

80.  Isocahedron  is  bounded  by  20  equilateral  triangles. 

81.  A  Conic  Section  is  formed  by  the  intersection  of  a  cone 
and   a  plane.     The   different   conic   sections   are   the   triangle, 
circle,  ellipse  parabola  and  hyperbola. 

82.  A  Triangular  Section  is  cut  from  a  cone  by  a  plane  through 
the  axis  perpendicular  to  the  base. 

,83.  Ellipse.  This  section  is  formed  when  the  cone  is  cut  by 
a  plane  oblique  to  its  opposite  elements.  An  oblique  section 
through  a  circular  cylinder  is  also  an  ellipse. 


STANDARD  DRAFTING  ROOM  CONVENTIONS  43 

84.  Parabola.     When  a  cone  is  cut  by  a  plane  parallel  to 
one  of  its  elements,  the  section  is  a  parabola. 

85.  Hyperbola.     When  a  cutting  plane  makes  an  angle  with 
the  base  greater  than  the  angle  made  by  an  element,  the  section  is 
a  hyperbola.     A  plane  parallel  to  the  axis  passed  on  either  side 
of  it  will  give  a  hyperbola. 

86.  Sphere.    A  solid,  the  surface  of  which  is  at  a  uniform 
distance  from  the  center. 

87.  Ungulas.     Cylindrical  ungulas  are  frusta  of  cylinders; 
conical  ungulas  are  frusta  of  cones. 

88.  Concave  means  hollow,  curved  inwardly  the  opposite  of 
Convex,  which  curves  outwardly,  bulging.    A  sphere  has  a  convex 
curve. 


CHAPTER  III 

FREEHAND  LETTERING  AND  GEOMETRICAL  DRAWING 

ONE  of  the  important  parts  of  a  commercial  working  drawing 
is  the- lettering  including  figures. 

If  a  drawing  is  well  made  but  poorly  lettered  and  dimen- 
sioned, it  looks  bad.  If  the  lettering  is  good  the  drawing  will 
have  a  good  appearance  even  if  it  has  defects  in  its  construction. 

All  lettering  and  figuring  must  be  placed  on  a  drawing  free- 
hand. Therefore,  it  is  necessary  to  give  all  the  time  and  effort 
required  to  become  as  proficient  as  possible  in  the  making  of 
good  freehand  letters  and  figures. 

In  Chapter  2,  Article  22  specifies  the  style  of  letters  to  be  used 
in  this  course.  This  style  has  been  selected  for  its  maximum  of 
legibility  considering  its  comparative  ease  of  construction. 

Heretofore  it  has  been  the  custom  of  the  writer  when  teaching 
mechanical  drawing  to  give  a  course  in  freehand  lettering  before 
any  drawing.  In  theory,  this  is  good  practice  because  it  enables 
the  student  to  letter  his  drawings  as  soon  as  they  are  made  and 
to  do  so  in  a  fairly  creditable  manner.  It  has  been  found,  how- 
ever, that  to  most  beginners  freehand  lettering  comes  hard  at 
first,  and  to  interpolate  a  drawing  occasionally  between  the 
plates  of  letters  has  proven  to  be  a  wise  procedure. 

The  following  method  of  teaching  freehand  lettering  for  use 
on  machine  or  other  working  drawings  is  simple,  brief  and  pro- 
duces most  excellent  results.  This  method  was  introduced  by 
the  writer  at  Armour  about  ten  years  ago  and  it  was  probably 
the  beginning  of  such  a  method  in  Chicago  at  least. 

The  value  of  freehand  lettering  cannot  be  emphasized  too 
much.  It  is  very  desirable  that  a  draftsman  should  be  able  to 
letter  and  figure  his  drawing  with  a  plain,  neat,  properly  formed, 
well-made  freehand  letter,  of  maximum  legibility  and  compara- 
tively easy  to  make. 

Many  "  ads  "  for  draftsmen  these  days  require  that  appli- 

44 


FREEHAND  LETTERING  AND  GEOMETRICAL  DRAWING  45 

cants  must  be  good  freehand  letterers,  so  it  is  well  worth  while 
to  spend  all  the  time  and  effort  necessary  to  become  a  good  let- 
terer  and  figurer. 

Straight-line  Letters.  The  straight-line  letters  are  taken  up 
first  because  they  are  comparatively  easy  to  make.  All  the  letters 
of  the  alphabet  both  straight  and  curved  will  be  drawn  6  spaces 
high,  that  is  f  "  (since  the  cross-section  pad  is  divided  8X8). 

This  large  letter  is  used  at  first  to  teach  the  form  and  pro- 
portion of  the  letter,  together  with  the  proper  slope  suitable  for 
the  height. 

PLATE  i.    4  HOURS 

Before  beginning  to  draw  the  letters,  prepare  the  4H  pencil, 
as  described  in  Article  4,  Chapter  i,  page  7,  and  illustrated  by 
Figs.  9,  10  and  n. 

This  plate  will  consist  of  two  sets  of  the  straight-line  letters 
of  the  alphabet.  The  second  set  must  show  a  decided  improve- 
ment over  the  first,  see  Fig.  7. 

When  ready  to  begin  drawing  the  letters  proceed  as  follows: 
Place  the  pad  on  the  drawing  board  in  front  of  you,  the  long  way 
from  left  to  right,  and  sitting  in  an  easy  position,  holding  the 
pencil  not  too  tightly  in  the  fingers,  with  the  elbow  close  to  the 
side,  locate  the  lowest  point  of  the  letter  "  /  "  12  spaces  from  the 
top  of  the  pad  and  7  spaces  from  the  left-hand  edge  of  the  sheet. 
Then  from  that  point  3  spaces  to  the  right  and  6  spaces  up  locate 
the  highest  point  of  this  letter  and  mark  it  with  the  point  of  the 
pencil.  Then  place  the  point  of  the  pencil  just  over  this  highest 
point  and  without  touching  the  paper  at  first,  draw  down 
towards  the  lowest  point  and  repeat  the  motion  a  few  times 
without  making  any  mark  on  the  paper. 

This  motion  is  for  the  purpose  of  obtaining  direction.  Then 
gradually  lower  the  pencil  point  and  touch  the  paper  lightly 
while  drawing  the  letter.  To  make  sure  that  the  line  of  the 
"  I  "  is  straight,  take  up  the  pad  and  look  at  the  line  edgewise, 
you  will  easily  detect  any  crookedness  or  curve.  If  it  should  not 
be  quite  straight,  erase  it  gently  with  the  Emerald  pencil  eraser, 
Fig.  30,  Article  16,  page  20,  and  try  again. 


46 


MECHANICAL  DRAWING 


But  if  you  find  it  straight,  then  proceed  to  draw  the  letter 
"  L  "  in  a  similar  manner. 

Locate  the  lowest  left-hand  point  of  the  "  L  "  3!  spaces  to 
the  right  of  the  lowest  point  of  the  "  /,"  then  3  spaces  to  the  right 
again  for  the  slope,  then  up  6  spaces  for  the  height  and  mark 
the  upper  point  of  the  "  L." 


-Si — I 


i- — S- 


7 

\ 

i 

y 

/- 

/  \  ^- 

y^i    '     • 

? 

x^- 

i 

... 

?- 

/L 

\ 

-f 

^* 

y 

v 

= 

(/- 

•y 

~v- 

/           / 

\ 

7 

/ 

g 

/ 

/ 

\ 

I 

3 

/ 

/  '  r* 

! 

*        ~j 

1 

/ 

, 

/ 

/ 

^  —  — 

\ 

K- 

— 

4 

. 

— 

:  i  ;  ,^— 

g 

~ 

2 

6 

:= 

=6 

f- 

~i 

'-' 

- 

r 

^^ 

fi~s 

— 

— 

7 

•\ 

7 

i 

7 

^ 

(- 

\ 

X 

"1* 

-/ 

4= 

!       ' 

/ 

/ 

s 

\ 

| 

1 

f 

~K 

-^ 

— 

- 

a 

i 

•t 

TT: 

— 

§ 

^__ 

C-. 

- 

2* 

1      1       1 

Ka- 

-4 
1    I 

7 

_ 

T- 

-j 

t- 

TJ 

- 

>— 

4 

}- 

-i 

*- 

-^ 

—  < 

— 

3 

— 

-. 

1 

i 

i—  - 

-e 

X 

4 

r 

\ 

-5  1 

-Uf| 

\]\ 

4 

/ 

~ 

, 

• 

7 

7- 

\ 

y 

y 

• 

^_ 

y 

* 

/ 

—i 

/ 
L 

4— 
•  —  —  9 

^1: 

? 

3 

^ 

I:: 

\ 

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T 

I' 

1 

3^ 

\ 

—  i 

i 

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~r 

—  -4 

t 

i 

•* 

i 

g 

1 

^- 

FIG.  38. 

Next  draw  the  down  stroke  of  the  "  L  "  as  was  done  in  draw- 
ing the  "  /." 

Then  draw  the  bottom  line  from  left  to  right  4!  spaces, 
and  so  on  for  all  the  straight-line  letters  according  to  their  form 
and  proportions  given  in  Fig.  38. 

When  all  the  letters  in  Plate  i  have  been  drawn  and  approved 
the  student  should  sign  his  name  in  the  lower  right-hand  corner 
together  with  plate  number,  the  current  date  and  also  the  time 
taken  to  make  the  plate,  counting  the  gross  time,  preparation, 
drawing,  etc.  (For  example) 

PLATE   1 

3  HOURS,  JULY  21,  1917. 
JAMES  GRISWOLP, 


FREEHAND  LETTERING  AND  GEOMETRICAL  DRAWING   47 

The  plate  will  then  be  signed  and  recorded  and  returned  to 
the  student  to  be  kept  flat  in  manilla  laboratory  covers  until 
all  the  lettering  plates  are  finished  when  they  are  to  be  bound 
together  in  the  cover  plates  with  brass  binders  and  a  title  let- 
tered on  the  outside  of  the  cover  as  follows: 

Mechanical  Drawing 

FREEHAND  LETTERING 

PLATES  1,  3,  AND  5  TO  10,  INCLUSIVE 

JULY  21,  1917 

HAROLD  DALE. 

31.  Geometrical    Drawing.     The    problems    in    geometrical 
drawing  are  given  for  several  reasons. 

1.  To  teach  the  use  of  drawing  instruments  and  at  the  same 
time  learn  the  methods  of  construction  of  those  problems  in 
practical  geometry  that  are  the  most  useful  in  mechanical  draw- 
ing, and  to  impress  them  upon  the  mind  of  the  student  so  that 
he  may  readily  apply  them  in  practice. 

2.  To  emphasize  accuracy  of  construction.     All  dimensions 
should  be  laid  off  carefully,  correctly  and  quickly  in  the  manner 
directed  in  Article  n,  page  17. 

3.  To  impress  upon  the  student  by  means  of  these  drawings 
that  straight  lines  joining  arcs  should  be  made  exactly  tangent 
so  that  the  joints  cannot  be  noticed, 

It  is  the  little  things  like  these  that  make  or  mar  a  drawing, 
and  if  attended  to  or  neglected  they  will  make  or  mar  the  drafts- 
man. The  constant  endeavor  of  the  student  should  be  to  make 
every  drawing  he  begins  more  accurate,  quicker  and  better  in 
every  way  than  the  preceding  one. 

A  drawing  should  never  be  handed  in  as  finished  until  the 
student  is  perfectly  sure  that  he  cannot  improve  it  in  any  way 
whatever,  for  the  act  of  handing  in  a  drawing  is  the  same,  or 
should  be  the  same,  as  saying  "  This  is  the  best  that  I  can  do;" 
"  I  cannot  improve  it;"  "  it  is  a  true  measure  of  my  ability  to 
make  this  drawing." 

32.  Straight-line      Problems     in     Geometrical     Drawings. 
Only  those  straight-line  problems  that  require  the  use  of  the 


48  MECHANICAL  DRAWING 

compass  and  spacer  have  been  selected  for  drawing  exercises  in 
this  plate.  Other  straight-line  problems  that  can  be  drawn 
directly  with  triangle  and  T-square  such  as  perpendiculars  to 
given  lines,  lines  parallel  to  one  another,  etc. 

PLATE   2.     6  HOURS 

To  prepare  for  drawing  the  problems  in  Plate  2. 

i  st.  Use  sheet  of  cream  detail  paper  referred  to  in  Article 
20,  page  22.  Lay  it  on  the  board  close  to  the  top  and  make  it 
even  with  the  T-square  held  rigidly  against  the  left-hand  end 
of  board  with  the  left  hand.  When  square  with  T-square  and 
board  insert  thumb  tack  in  each  upper  corner.  If  the  paper 
curls  up  at  first  at  the  lower  corners  insert  a  thumb  tack  at  each 
of  the  lower  corners  also.  After  a  while  when  the  paper  will  lie 
flat  without  the  lower  thumb  tacks  take  them  out.  They  should 
be  removed  anyway  when  drawing  with  the  T-square  at  the 
bottom  of  the  sheet. 

2d.  Get  out  the  4.H  and  6H  pencils,  pencil  compass,  dividers, 
the  two  triangles,  emerald  eraser  and  pencil  pointer. 

3d.  Put  straight-line  pencils  and  compass  pencil  in  good  order 
as  directed  in  Article  4,  page  7. 

4th.  Draw  border  line  on  the  drawing  paper  as  follows: 
Take  the  scale  shown  in  Fig.  24,  page  17,  and  using  the  edge  of 
T^ths,  lay  off  \" — that  is  half  an  inch — from  the  top  and  bottom 
edges  of  the  paper,  and  with  the  T-square  and  4H  pencil  held  as 
illustrated  in  Figs.  3  and  4,  draw  straight  lines  from  left  to  right, 
leaning  very  lightly  on  the  pencil,  so  as  not  to  form  a  groove  in 
the  paper.  Then  lay  off  if"  from  the  left-hand  edge  at  the  top 
and  bottom  and  using  the  T-square  as  a  straight  edge,  draw  the 
left-hand  border  line.  Next  lay  off  \"  from  the  right-hand  edge 
of  the  paper  about  2"  from  the  top  and  bottom  and  using  the 
T-square  as  before  draw  the  right-hand  border  line. 

5th.  Lay  out  the  sheet  inside  the  border  lines  in  16  equal 
parts,  as  follows.  Divide  the  long  space  between  the  left-  and 
right-hand  border  lines  which  is  equal  to  18"  by  4  making  4^". 
Set  the  large  dividers,  Fig  20,  page  13,  to  4^"  and  step  off  4 
spaces  on  the  upper  border  line  from  left  to  right,  and  mark  the 


FREEHAND  LETTERING  AND  GEOMETRICAL  DRAWING   49 


divisions  with  the  point  of  the  pencil.     Through  these  points 
draw  vertical  lines  with  the  T-square  and  largest  triangle  held 


in  a  similar  manner  to  that  shown  in  Fig.  3.  Divide  the  space 
between  the  top  and  bottom  border  lines  into  4  equal  spaces  in 
the  same  way. 


50 


MECHANICAL  DRAWING 


PROB.  i,  FIG.  40.     Bisect  a  Given  Finite  Straight  Line. 

i  st.  Using  the  6H  pencil  sharpened  as  described  in  Article  4, 
page  7,  and  the  T-square,  draw  the  given  line  AB  3}"  long  in 
the  center  of  the  first  space  on  the  sheet.  Letter  the  ends  of  the 
line  A  and  B  very  lightly  and  carefully  with  the  4!!  pencil  sharp- 
ened as  directed  in  Section  4. 

2d.  Take  the  large  compass  and  set  it  to  a  radius  greater 
than  half  the  length  of  AB,  say  2"  and  placing  the  needle  point 
at  A  and  B,  respectively,  draw  small  arcs  intersecting  or  cutting 
each  other  at  E  and  F. 

3d.  With  one  of  the  triangles  used  as  a  straight  edge,  draw  a 


FIG.  41, 


fine,  narrow  line  through  the  points  of  intersection  of  the  two 
small  arcs  at  E  and  F,  cutting  AB  at  C.  At  the  point  C  the  line 
AB  is  bisected,  or  divided  into  two  equal  parts.  An  arc  of  a 
circle  may  be  bisected  in  the  same  way.  Great  care  should  be 
taken  when  drawing  the  line  through  E  and  F  to  make  sure  that 
it  passes  exactly  through  the  point  of  intersection.  It  is  some- 
times a  good  plan  to  locate  the  exact  point  of  intersection  with 
the  point  of  the  4!!  pencil  before  drawing  the  line  through  EF. 
Leave  this  drawing  in  fine  lines  for  the  present  and  proceed  next 
to  make  the  drawing  in  Fig.  41. 

PROB.  2,  FIG.  41.     Bisect  a  Given  Angle  by  Dividing  it  into 
Two  Equal  Angles. 


FREEHAND  LETTERING  AND  GEOMETRICAL  DRAWING   51 

i st.  Assume  the  point  A,  Fig.  41,  in  the  up-and-down  center 
of  second  space  on  the  sheet  \"  from  the  left  division  line  and 
mark  it  A.  From  A  draw  the  given  angle  BAG  making  the  legs 
AB  and  AC  about  2§"  long. 

2d.  With  the  point  A  as  center  and  a  radius  about  if"  long 
draw  an  arc  cutting  the  legs  of  the  angle  in  the  points  C  and  B. 

3d.  With  B  and  C  as  centers  draw  arcs  cutting  in  D. 

4th.  Through  the  points  A  and  D  draw  a  line  dividing  the 
given  angle  into  two  equal  angles. 

PROB.  3,  FIG.  42.  To  Bisect  an  Angle  when  the  Lines  form- 
ing the  Angle  do  not  Extend  to  a  Meeting  Point. 


FIG.  43. 


i  st.  Draw  AB  and  FG,  making  any  convenient  angle  with 
each  other,  locating  them  in  the  3d  space  about  as  shown  in 
Fig.  39- 

2d.  Draw  the  line  CD  parallel  to  AB  and  J"  from  it.  Draw 
the  line  CV  parallel  to  FG,  and  produce  them  to  meet  at  the 
point  C. 

3d.  Bisect  the  angle  DCV  by  Prob.  2.  The  bisector  CH 
will  also  bisect  the  angle  between  the  given  lines  AB  and  FG. 

PROB.  4,  FIG.  43.  From  a  point  on  a  given  line  set  of  an 
angle  equal  to  a  given  angle. 

Let  BAC  be  the  given  angle  and  D  the  given  point  on  given 
line  DC. 


52 


MECHANICAL  DRAWING 


ist.  Draw  the  line  AB  3"  long  and  3"  above  the  bottom  of 
space  4  and  from  the  point  A  draw  the  line  AC  making  an  angle 
of  30°  with  AB  using  the  3o°X6o°  triangle. 

2d.  With  a  radius  of  3^"  and  the  point  A  as  center  draw  arc 
BC.  From  D  as  center  and  the  same  radius  draw  arc  EF. 
With  center  E  and  radius  BC  cut  arc  EF  in  F. 

3d.  Through  the  D  and  F  draw  Z)F.  The  angle  EDF  is 
equal  to  the  given  angle  BA  C. 

PROB.  5,  FIG.  44.     Construct  a  rhomboid  having  adjacent  sides 


1    2    3  4.  6  6   7   8  9  10  11 1213  1J/. 
FlG.  45. 


equal  to  two  given  lines  A  B  and  CD,  and  an  angle  equal  to  a  given 
angle  A. 

ist.  Draw  the  given  line  AC  %"  from  the  top  of  the  5th  space 
and  make  if"  long. 

2d.  Draw  AB  J"  below  AC  2%"  long. 

3d.  Draw  the  angle  A  equal  to  30°. 

4th.  Draw  the  line  DE  |"  above  bottom  of  space  equal  in 
length  to  line  AB. 

5th.  With  D  on  the  line  DE  as  center  and  any  convenient 
radius,  say  i",  describe  an  arc  and  make  the  angle  at  D  equal  to 
the  given  angle  A.  Make  DF  equal  in  length  to  AC. 

6th.  From  F  with  a  radius  equal  in  length  to  the  given  line 
AB  and  from  E  with  a  radius  equal  to  the  given  line  AC  describe 
arcs  intersecting  each  other  at  G.  Join  FG  and  EG  with  straight 
lines  completing  the  rhomboid  as  required. 


FREEHAND  LETTERING  AND  GEOMETRICAL  DRAWING    53 


It  will  do  no  harm  at  this  point  to  remind  the  student  that 
all  the  lines  in  these  drawings  must  be  made  sharp  and  narrow — 
not  faint  and  weak.  This  can  be  done  by  maintaining  the  pencil 
points  in  good  order  as  already  explained.  Make  an  effort  to 
obtain  neatness  and  extreme  accuracy  of  construction  in  all  your 
work,  especially  in  locating  centers  of  arcs  and  in  drawing  lines 
through  points  of  intersection. 

PROB.  6,  FIG.  45.  Divide  a  given  line  into  any  number  of 
equal  parts.  AB  is  the  given  line.  Divide  it  into  15  equal  parts. 


c  1    2.  3  4   56    7  8.  9  10 11  It  13  U 

FIG.  46. 


FIG.  45  a. 


ist.  Draw  the  given  line  AB  if"  above  the  bottom  line  of 
the  space,  and  make  2"  long. 

2d.  Draw  another  line  CD  parallel  to  AB  and  i"  below  it. 
Make  this  3%"  long. 

3d.  From  C  on  the  line  CD  set  off  the  number  of  equal  parts 
into  which  the  line  A  B  is  to  be  divided. 

4th.  Draw  lines  through  CA  and  DB  and  produce  them  until 
they  meet  at  E. 

5th.  Through  each  one  of  the  points  i,  2,  3,  4,  etc.,  draw  lines 
to  the  point  E,  dividing  the  line  AB  into  the  required  number  of 
equal  parts. 

This  problem  is  useful  in  dividing  a  line  when  the  point  re- 
quired is  difficult  to  find  accurately — for  example  in  Fig.  450  AB 
is  the  circular  pitch  of  the  spur  gear,  partly  shown,  which  includes 
a  space  and  a  tooth  and  is  measured  on  the  pitch  circle. 


54 


MECHANICAL  DRAWING 


In  cast  gears  the  space  is  made  larger  than  the  thickness  of 
the  tooth,  the  proportion  being  about  6  to  5 — that  is,  if  we  divide 
the  pitch  into  eleven  equal  parts  the  space  will  measure  TBT  and 
tooth  TT.  The  TT  which  the  space  is  larger  than  the  tooth  is 
called  the  backlash. 

Let  A'B' ',  Fig  450,  be  the  pitch  chord  of  the  arc  AB. 

Draw  CD  parallel  to  A'Bf  at  any  convenient  distance  and 
set  off  upon  it  eleven  equal  spaces  of  any  convenient  length. 

Draw  CA'  and  DB'  intersecting  at  E. 

From  point  5  draw  a  line  to  E.  This  line  divides  A'B'  as 
required. 

The  one  part  TT  and  the  other  TT. 


FIG.  47. 


PROB.  7,  FIG.  47.     Draw  an  equilateral  triangle  on  a  given  base. 

i  st.  Draw  the  given  base  J"  above  the  bottom  of  the  space 
and  from  the  points  A  and  B  with  AB  as  radius  describe  arcs 
cutting  in  C. 

2d.  Draw  lines  AC  and  BC.  The  triangle  ABC  is  equi- 
lateral and  equiangular. 

PROB.  8,  FIG.  48.  Construct  an  equilateral  triangle  of  a  given 
altitude  AB. 

i  st.  Assume  the  altitude  AB  and  at  both  ends  of  it  draw 
lines  perpendicular  to  it  as  CA ,  DB. 

2d.  From  A  with  any  radius  describe  a  semicircle  on  CA,  and 
with  its  radius  cut  off  arcs  i,  2. 


FREEHAND  LETTERING  AND  GEOMETRICAL  DRAWING  55 

36.  Draw  lines  from  A  through  i  and  2  and  produce  them 
until  they  cut  the  base  BD. 

PROB.  9,  FIG.  49.     Trisect  a  right  angle. 

i  st.  Draw  the  line  CB  2j"  long,  |"  above  the  bottom  of  the 
9th  space.  With  the  right-angled  triangle  3o°X6o°  draw  the 
perpendicular  BA  2%"  long,  completing  the  given  right  angle. 

2d.  With  B  as  center  and  BC  as  radius  describe  the  arc  AC. 

3d.  With  the  same  radius  and  centers  A  and  C  cut  the  arc 
AC  in  points  i  and  2.  Draw  lines  from  i  and  2  to  B.  These 
lines  divide  the  right  angle  into  3  equal  angles. 


FIG.  49- 

PROB.  10,  FIG.  50.     Draw  a  pentagon  on  a  given  side  AB. 

A  pentagon  is  a  five-sided  figure  and  is  often  met  with  in 
practice. 

i  st.  Draw  AB  if"  long  \"  above  the  bottom  of  the  space  and 
produce  it  to  the  left. 

2d.  With  B  as  center  and  radius  BA,  draw  the  semicircle 
€2  A. 

3d.  With  center  A  and  same  radius  draw  arc  BD,  cutting 
first  arc  in  the  point  D.  Bisect  AB  in  E  and  through  it  draw 
ED,  which  will  be  perpendicular  to  AB. 

4th.  Bisect  arc  BD  in  the  point  F  and  draw  EF,  then  with 
center  C  and  radius  EF  cut  off  arcs  Ci  and  1-2  on  the  same 
semicircle. 

5th.  Draw  line  £2;  it  will  be  a  second  side  of  the  pentagon. 


56 


MECHANICAL  DRAWING 


Bisect  it  and  draw  a  line  through  the  point  of  bisection  perpen- 
dicular to  B2. 

The  perpendiculars  through  AB  and  B2  cut  in  G,  which  is 
the  center  of  the  circumscribing  circle  of  the  pentagon. 

PROB.  n,  FIG.  51.     Construct  a  heptagon  on  a  given  side  AB. 

A  heptagon  is  a  seven-sided  figure. 

ist.  Draw  AB  \"  above  the  bottom  of  the  space  ij"  long  and 
produce  it  to  the  left. 


FIG.  50. 


FIG.  51. 


2d.  With  center  B  and  radius  BA  describe  a  semicircle, 
and  with  A  as  center  and  same  radius  draw  arc  cutting  the  semi- 
circle in  D. 

3d.  Bisect  AB  in  E  and  draw  the  perpendicular  ED. 

4th.  With  C  as  center  and  ED  as  radius,  cut  off  arc  Ci  on 
the  semicircle  and  draw  Bi\  it  is  a  second  side  of  the  heptagon. 

5th.  Bisect  Bi  and  obtain  the  center  circumscribing  circle 
and  finish  drawing  the  heptagon  as  in  the  preceding  problem. 

These  operations  must  be  very  carefully  made  to  obtain  an 
accurate  construction  of  the  figure. 

PROB.  12,  FIG.  52.  Construct  a  regular  octagon  on  a  given 
line  AB. 

ist.  Draw  AB  if"  long  \"  above  bottom  of  space  and 
extend  in  both  directions. 


FREEHAND  LETTERING  AND  GEOMETRICAL  DRAWING    57 


2d.  Erect  perpendiculars  at  A  and  B. 

3d.  With  centers  A  and  B  and  radius  AB  describe  the 
semicircles  CEB  and  AFD. 

4th.  Bisect  the  quadrants  CE  and  DF  in  i  and  2,  then 
A  i  and  B2  will  be  two  more  sides  of  the  octagon. 

5th.  At  i  and  2  erect  perpendiculars  1-3  and  2-4  equal 
to  AB.  Draw  1-2  and  3-4. 

6th.  Make  the  perpendiculars  at  A  and  B  equal  to  1-2  or 


C 

FIG.  53. 


3-4,   viz.,   ^5   and   ^46.     Complete   the  octagon  by  drawing 

3~5>  5~6  and  6-4- 

PROB.  13,  FIG.  53.  Construct  a  regular  polygon  of  any 
number  of  sides  the  circumscribing  circle  being  given. 

i st.  Draw  a  horizontal  center  line  if"  above  bottom  of 
space  and  at  the  center  of  it  draw  a  vertical  center  line  and  at 
the  point  of  intersection  describe  the  given  circle  of  i|"  radius. 

2d.  At  any  point  of  contact  as  C  draw  a  tangent  AB  to 
the  given  circle. 

•3d.  From  C  with  any  convenient  radius  describe  a  semi- 
circle cutting  the  given  circle. 

4th.  Divide  the  semicircle  into  as  many  equal  parts  as 
the  polygon  is  required  to  have  sides,  as  i,  2,  3,  4,  5,  6. 

5th.  Through  each  division  draw  from  C  lines  to  cut  the 
circle  in  points  of  the  hexagon.  Join  these  points  with  straight 
lines  and  complete  the  figure. 


58 


MECHANICAL  DRAWING 


PROB.  14,  FIG.  54.     Draw  a  right  line  equal  to  half  the  cir- 
cumference of  a  given  circle. 

ist.  Draw  a  vertical  diameter  AB  3"  long  and  if"  from 
the  left. 

2d.  Draw  the  horizontal  center  line  in  center  of  the  space 
and  describe  the  3"  given  circle. 

3d.  Draw  AC  perpendicular  to  AB  and  eqal  to  3  times 
the  radius  of  the  circle. 

4th.  At  B  draw  BE  perpendicular  to  AB. 

,     G 

A  c  " 


5th.  With  B  as  center  and  radius  of  the  circle  cut  off  arc 
BD,  bisect  it  and  draw  a  line  from  center  of  circle  through 
the  bisection,  cutting  the  line  BE  in  E. 

6th.  Join  EC.  Line  EC  will  be  equal  to  half  the  circum- 
ference of  the  given  circle. 

PROB.  15,  FIG.  55.  Find  a  mean  proportional  to  two  given 
right  lines  AB  and  CD. 

ist.  Draw  AB  2"  long  ij"  above  the  bottom  line  of  the 
space  and  locate  the  point  A  \"  from  the  left. 

2d.  Draw  CD  1%"  long,  J"  below  AB. 

3d.  Extend  the  line  AB  to  E,  making  BE  equal  to  CD. 

4th.  Bisect  AE  in  F  and  from  F  with  radius  FA  describe 
a  semicircle. 

5th.  At  B  where  the  two  given  lines  join  erect  a  perpen- 
dicular to  AE  cutting  the  semicircle  in  G. 

BG  will  be  a  mean  proportional  to  CD  and  AB. 


FREEHAND  LETTERING  AND  GEOMETRICAL  DRAWING   59 

Important 

When  the  problems  in  Plate  2  have  been  completed  in 
fine  pencil  lines  and  approved,  the  plate  should  be  cleaned 
with  the  art  gum  and  then  all  the  given  and  required  lines 
strengthened  with  the  4H  pencil  sharpened  as  directed  in 
Art.  4. 

The  problem  numbers  should  then  be  neatly  lettered  in 
the  lower  right-hand  corner  of  each  space.  The  height  of 
the  letters  to  be  ^"  and  the  numbers  -fa". 

A  title  like  the  standard  title,  Fig.  35,  page  24,  should  then 
be  drawn  carefully  in  pencil  and  when  all  the  lettering  has 
been  approved,  the  border  line  and  all  lettering  should  then 
be  inked  in,  and  the  drawing  signed  and  recorded. 

Since,  as  has  been  already  emphasized  the  lettering  and 
figures  must  be  neat  and  well  made,  it  will  be  best  to  defer 
lettering  the  early  drawing  plates  until  after  the  4th  plate 
of  lettering  has  been  finished.  The  student  by  that  time 
should  be  able  to  make  fairly  good  lettering  and  the  lettering 
on  his  drawing  plates  will  be  done  with  greater  facility. 
Every  succeeding  plate  will  be  another  opportunity  to  prac- 
tice his  lettering  and  to  show  how  much  he  has  profited  by 
his  study  and  practice  of  the  first  four  letter  plates. 

Making  the  Title 

i st.  Draw  all  guide  lines  fine  and  narrow. 

2d.  Letter  on  a  separate  paper  the  longest  line  in  the  title 
as  "  Armour  Institute  of  Technology,"  and  measure  its  length 
then  from  •&"  inside  the  right-hand  border  line,  lay  off  that 
length  to  the  left  and  letter  that  line  first,  when  done,  bisect 
it  and  draw  a  light  line  through  the  point  of  bisection  that 
will  be  the  center  line  of  the  title  and  the  remainder  of  the 
title  should  be  balanced  with  reference  to  that  center  line. 

3d.  Submit  the  title  for  approval. 

4th.  Ink  the  title  and  make  the  letters  in  the  words  of 
the  main  title  as  "  Geometrical  Drawing,"  very  heavy  so 


60  MECHANICAL  DRAWING 

that  they  will  be  emphasized  and  stand  out  from  the  rest. 
Do  not  forget  that  numbers  combined  with  letters  are  to  be 
taller  than  the  letters. 

The  next  plate  of  lettering  will  consist  of  the  curved  letters 
of  the  alphabet  and  since  they  are  more  difficult  to  make 
than  the  straight-line  letters  more  pains  will  be  required  to 
obtain  the  desired  result. 

PLATE  3.    FIG.  56.    6  HOURS 

These  letters  are  to  be  drawn  6  spaces  high  and  it  will  be 
seen  from  Fig.  56  that  two  sets  of  the  curved  letters  of  the 
alphabet  are  required.  The  second  set  ought  to  show  a 
decided  improvement  over  the  first.  The  curves  should  be 
carefully  analyzed  as  to  their  true  form  and  proportion  given 
in  Fig.  56. 

Submit  each  letter  as  soon  as  drawn  for  criticism  and 
correction.  In  this  way  the  art  of  obtaining  good  truly 
formed  letters  will  be  acquired  much  quicker  than  if  several 
letters  are  made  before  having  them  examined  and  criticized. 
The  curves  of  all  the  letters  in  this  plate  are  similar  so  if  the 
first  letters  are  well  made  and  the  curves  understood  the 
succeeding  letters  will  be  easier  to  make  and  show  improve- 
ment. 

With  a  proper  appreciation  of  the  extreme  importance  of 
being  able  to  make  good  freehand  lettering  and  a  close  appli- 
cation to  work  this  plate  should  be  finished  within  the  number 
of  hours  allowed  for  it. 

Prepare  to  draw  these  curved  letters  in  a  similar  manner 
to  the  way  described  in  Article  32. 

Using  the  cross-section  pad  and  4!!  pencil  as  before  begin 
drawing  the  letter  "  U  "  as  follows: 

First  draw  the  two  guide  lines  marked  A  and  B,  giving 
them  the  required  slope  of  three  spaces. 

Beginning  at  the  point  i,  draw  the  narrow  curve  down- 
ward until  tangent  to  the  bottom  line  at  3.  Lift  the  pencil 
and  commence  the  downward  stroke  of  the  larger  curve  at 


FREEHAND  LETTERING  AND  GEOMETRICAL  DRAWING   61 


I 


J 


k 


fel 


J 


62  MECHANICAL  DRAWING 

the  point  2,  drawing  a  smooth,  even  curve  until  tangent  at 
the  point  3. 

Press  very  lightly  with  the  pencil  and  try  to  obtain  a 
narrow,  smooth  line. 

The  "J  "  is  quite  similar  to  the  "  U,"  it  is  a  little  nar- 
rower, therefore,  the  curves  are  slightly  shorter. 

When  ready  to  draw  the  curve  of  the  "  0  "  begin  at 
point  4  and  draw  down  and  to  the  left,  making  it  tangent 
to  the  guide  lines  at  the  points  5  and  6. 

Then  from  4  again,  draw  to  the  right  and  down  to  6. 

By  studying  carefully  where  the  curves  cross  the  vertical 
and  horizontal  lines  of  the  cross-section  paper  it  should  not 
take  long  to  obtain  the  true  form. 

Note  that  the  curve  in  the  upper  right-hand  corner  of  the 
"  P,"  "  B,"  :l  R  "  and  "  D  "  is  the  same  kind  of  a  narrow  curve 
in  all  of  them.  The  lower  curve  in  these  letters  is  of  the 
same  nature  as  the  lower  right-hand  curve  in  the  others. 

•  It  should  be  noticed  in  the  letter  "  S  "  that  the  upper 
half  is  a  little  smaller  than  the  lower  half  and  that  the  top 
and  bottom  curves  are  flatter  than  the  curves  of  any  of  the 
other  letters. 

37.  Geometrical  Drawing.     Continued. 

PLATE  4,  FIG.  57.    8  HOURS 

This  plate  is  to  consist  of  12  geometric  problems  involving 
the  use  of  the  compasses  as  well  as  the  triangles  and  T-- 
square. Included  are  figures  of  the  conic  sections  and  other 
curves. 

PROB.  1 6,  FIG.  58.    Find  the  center  of  a  given  arc. 

ist.  Draw  an  arc  with  a  2^"  radius.  Center  of  arc  to  be 
J"  above  bottom  line  of  space. 

2d.  Draw  chords  AB  and  EC  and  bisect  them. 

3d.  Produce  bisectors  to  meet  in  center  required. 

PROB.  17.     FIG.  59.     Draw  the  involute  of  a  circle. 

ist.  Draw  the  given  circle  with  \"  radius  center  2}"  above 
bottom  line  and  3!  from  left  line  of  the  space. 


FREEHAND  LETTERING  AND  GEOMETRICAL  DRAWING    63 


2d.  Divide  the  circle  into   12  equal  parts  with  the  2   tri- 
angles and  T-square  and  draw  radii. 


3d.  Draw  tangents  at  right  angles  to  the  radii. 
4th.  On  the  tangent  to  radius  i  lay  off  a  distance  equal 
to  one  of  the  parts  into  which  the  circle  is  divided. 


64 


MECHANICAL  DRAWING 


5th.  On  each  of  the  tangents  set  off  the  number  of  parts 
corresponding  to  the  number  of  the  radii.  Tangent  12  will 
be  the  circumference  of  the  circle  unrolled,  and  the  curve 


FIG.  58. 


drawn  through  the  extremities  of  the  other  tangents  will  be 
the  involute  required. 

The  curve  may  be  drawn  with  arcs  of  circles,  thus:  Take 
i  as  center  and  1-12  as  radius  and  draw  arc  12-!,,  then 
with  2  as  center  and  2-L  as  radius  'draw  arc  L-K  and  so  on 
around  the  circle. 

PROB.  1 8.  FIG.  60.  Draw  an  ellipse  with  a  given  major 
axis  AB  and  minor  axis  CD. 

The  ellipse  is  a  conic  section.     See  Fig. 

i st.  Draw  the  major  axis  3^"  long  in  the  vertical  center 
of  the  next  space  and  the  minor  axis  2\"  long  2"  from  the 
left  division  line. 

2d.  With  center  C  and  radius  AE  cut  AB  in  F  and  F'  the 
foci. 

3d.  Divide  EF  into  any  convenient  number  of  parts,  say 
7  as  i,  2,  3,  4,  etc. 

4th.  With  F  as  center  and  Ai  as  radius,  draw  a  short  arc 
above  and  below  the  horizontal  center  line  about  where  the 
curve  of  the  ellipse  would  be  likely  to  come  and  F'  as  center, 
same  radius  draw  small  arcs  on  the  other  side  of  the  minor 
axis.  Then  with  Bi  as  radius  draw  from  F  and  F'  as  centers 


FREEHAND  LETTERING  AND  GEOMETRICAL  DRAWING    65 

arcs  cutting  the  former  arcs  in  points  in  the  curve  of  the 
ellipse.  Repeat  the  process  from  i  to  7.  To  obtain  a  point 
in  the  curve  between  R  and  B  take  an  extra  division  between 
6  and  7  for  radii. 

5th.  Draw  the  curve  through  the  points  of  intersection  of 
the  arcs  as  at  S  and  R,  etc.,  either  with  the  irregular  curve 


FIG.  60. 


shown  in  Fig.  28,  or  by  arcs  of  circles  found  in  the  manner 
described  in  the  next  problem. 

The  above  method  of  finding  points  in  the  curve  of  the 
ellipse  is  theoretically  correct,  but  the  following  method  gives 
an  approximation  almost  as  close  as  can  be  drawn  for  small 
ellipses. 

PROB.  19.  FIG.  61.  Given  the  major  and  minor  axes  draw 
an  ellipse  by  the  following  close  approximent  method. 

i st.  Draw  major  and  minor  axes  as  before  locating  them 
about  as  shown  in  Plate  4. 

2d.  Draw  any  convenient  angle  like  that  shown  in  No.  2 
and  with  radius  equal  to  half  the  minor  axis  and  point  H 
as  center  draw  arc  LM  and  with  radius  equal  to  half  the 
major  axis  and  same  center  draw  arc  NO.  * 

3d.  Draw  the  right  line  LO  and  through  M  and  N,  re- 
spectively, draw  lines  M K  and  NP  parallel  to  LO. 

4th.  With  C  and  D  as  centers  and  radius  =  HP  mark 
the  points  i  and  i'  on  the  minor  axis  and  from  A  and  B 
with  a  distance  equal  to  H  K  lay  off  the  points  2  and  2'  on 
the  major  axis.  Then  with  centers  i,  i',  2,  and  2'  and  radii 
iD  and  2 A,  draw  arcs  of  circles  as  shown  in  Plate  4. 


66 


MECHANICAL  DRAWING 


5th.  To  complete  the  ellipse  between  these  arcs  of  circles 
use  a  piece  of  tracing  cloth  like  that  shown  at  T  in  Fig.  61, 
draw  a  narrow  line  in  the  center  of  it  on  the  dull  side  of  the 
cloth  and  puncture  a  small  hole  at  G.  From  G  lay  off  GF 
equal  to  the  semi-minor  axis  a'nd  GE  equal  to  the  semi- 
major  axis. 

6th.  Place  the  point  F  on  the  major  axis  and  point  E  on 
the  minor  axes  and  move  the  strip  of  tracing  cloth  so  that 
the  point  E  is  always  in  contact  with  the  minor  axis  and 
point  F  with  the  major  axis  when  the  necessary  points  may 
be  marked  through  the  puncture  at  G  with  the  sharp-pointed 
4H  pencil  and  the  curve  of  the  ellipse  completed  in  this  manner. 


Q 


FIG.  61. 

If  tracing  cloth  is  not  at  hand  use  a  card  or  piece  of  stiff 
paper  and  mark  the  points  G}  F  and  E  on  its  edge. 

Instead  of  using  the  above  method  to  complete  the  curve 
of  the  ellipse,  an  arc  of  a  circle  may  be  used  which  is  a  very 
close  approximation  to  the  correct  curve.  Add  the  half  of 
the  major  axis  to  the  half  of  the  minor  axis  and  divide  by  2, 


that  is 


the  radius  of  the  arc  whose 


center  may  easily  be  found  by  trial. 

PROB.  20.  FIG.  62.  Given  the  same  axes  draw  an  ellipse  by 
the  following  method. 

ist.  -With  A  as  center  and  radii  AB  and  AC  describe 
circles.  Draw  any  convenient  radii  as  ^3,  A 4,  etc. 

2d.  Make  3-1,  3-4,   etc.   perpendicular  to   AB,  and  £2, 


FREEHAND  LETTERING  AND  GEOMETRICAL  DRAWING   67 


FIG.  62 


£5,   etc.,  parallel  to   AB.    Then  i,  2,  5,  etc.,  are  points  on 

the  curve.    Draw  the  whole  ellipse. 

PROB.  21.    FIG.  63.    Given  the  directrix  BD  and  the  focus 

€,  draw  a  parabola  and  a  tangent  to  it  at  the 

point  3. 

The  parabola  is  a  curve   such   that  every 

point  in  the  curve  is  equally  distant  from  the 

directrix  BD  and  the  focus  C.     The  vertix  E 

is  equally  distant  from  the  directrix  BD  and 

the  focus  C,  that  is  CE,  is  equal  to  EB.    Any 

line  parallel  to  the  axis  is  a  diameter.     A  straight  line  drawn 

across  the  figure  at  right  angles  to  the  axis  is  a  double  ordi- 
nate, and  either  half  of  it  is  an 
ordinate.  The  distance  from  C 
to  any  point  on  the  curve,  as 
2  is  always  equal  to  the  hori- 
zontal distance  from  that  point 
to  the  directrix.  Thus  Ci  is 
F  equal  to  i  i',  €2  to  2  2',  etc. 
To  make  the  drawing: 

ist.  Draw  the   axis  AB  in 


the    center    of    the    space,   3" 
long,  and  extend  to  F. 

2d.  At  B  draw  BD  the  di- 
rectrix at  right  angles  to  AB. 

3d.  Draw  parallels  to  BD  through  any  points  in  AB  such 
as  i  i,  2  2,  etc. 

4th.  Locate  the  focus  C;  f  "  from  B  and  bisect  BC  in  E, 
the  vertix. 

5th.  With  C  as  a  center  and  a  distance  equal  to  i  i', 
cut  the  parallel  in  the  points  i  and  i.  Then  with  the  same 
center  and  distance  equal  to  2  2'  in  the  points  2  and  2  and 
so  on  for  the  other  points  in  the  curve. 

6th.  To  draw  the  tangent  at  the  point  3.  Make  EF  equal 
to  the  distance  of  ordinate  3  3  from  E.  Draw  the  tangent 
through  3  F. 

PROB.  22.    FIG.  64.    Describe  an  ionic  volute. 


FIG.  63. 


68 


MECHANICAL  DRAWING 


When  the  volute  is  to  be  drawn  to  a  given  height.  Divide 
the  given  height  into  seven  equal  parts,  and  through  the  point 
3  draw  3,  3  perpendicular  to  AB.  The  eye  of  the  volute 
the  small  circle  NP  should  be  made  equal  in  diameter  to  one 
of  the  divisions  on  AB. 

To  describe  the  method  of  drawing  the  curves  of  the 
volute  a  small  part  to  an  enlarged  scale  will  be  drawn. 

i  st.  In  the  center  of  4  spaces  draw  the  eye  of  the  volute 
2"  diameter  (see  Plate  4)  and  draw  the  axes  NN  and  PM. 

2d.  Inscribe  the  square  NPNM.  Bisect  its  sides  and  draw 
the  square  n,  12,  13,  14.  Draw  its  diagonals  u,  13  and  12,  14. 


FIG.  64. 

3.  Divide  the  half  diagonal  o,  12  into  3  equal  parts  and 
subdivide  each  of  these  into  4  parts  making  12  divisions  in 
all  from  o  to  12. 

4th.  At  the  second*  division  from  o  drop  a  perpendicular 
to  the  diagonal  n,  13,  and  from  where  it  cuts  the  diagonal 
draw  a  horizontal  to  cut  the  axis  PM  in  the  point  i  which  is 
the  first  center  of  the  outer  curve  of  the  volute. 

5th.  Through  the  point  i  draw  a  horizontal  line.  Through 
the  4th  division  on  line  o,  13  draw  a  horizontal  line  to  inter- 
sect diagonal  n,  13  at  point  3  from  3  drop  a  perpendicular 
to  meet  the  horizontal  through  i,  at  the  point  2.  Through 
2  draw  a  line  downward  parallel  to  diagonal  12,  14.  Point  2 


FREEHAND  LETTERING  AND  GEOMETRICAL  DRAWING   69 

is   the   second   center   of   the  volute  outer  curve.     The   other 
centers  3,  4,  etc.,  are  evident. 

6th.  From  the  first  division  on  line  o,  12  drop  a  perpen- 
dicular to  meet  diagonal  n,  13.     Through  the  point  of  inter- 


FIG.  65. 

section  draw  a  horizontal  to  cut  the  line  through  i  parallel 
to  diagonal  n,  13,  in  a  point  which  is  the  first  center  of  the 
inner  curve  of  the  volute  shown  as  a  broken  line  in  Plate  4. 
The  other  centers  will  be  found  by  following  around  the 
dotted  squares. 

PROB.  23.  FIG.  65.  Draw  an  hyperbola  having  a  given 
diameter  AB,  abscissa  BD  and  double  ordinate  EF. 

ist.  Draw  the  center  line  ABD  about  4"  long  and  make 
AB  equal  to  f"  in  the  center  of  the  space. 

2d.  Draw  FE  \\"  from  B  and  complete  the  rectangle  4FE, 
making  F^  parallel  and  equal  to  BD,  and  DF  equal  to  ij". 

3d.  Divide  DF  and  F^  into  the  same  number  of  equal 
parts,  and  from  B  draw  lines  to  the  points  in  ^F}  and  from 
A  draw  lines  to  the  points  in  DF. 

4th.  Draw  the  curve  through  the  points  where  the  lines 
correspondingly  numbered  intersect  each  other.  Repeat  below 
the  other  half  of  the  curve  as  indicated. 

PROB.  24.  FIG.  67.  To  draw  the  epicycloid  and  the  hypo- 
cycloid. 

i st.  Draw  the  arc  BC  with  a  radius  equal  to  3!",  using 
two  spaces  on  the  drawing  paper. 

2d.  In  the  most  convenient  position  draw  the  line  AF  and 


MECHANICAL  DRAWING 


with  a  radius  equal  to  -f^"  describe  the  generating  circles  FC 
and  CG  tangent  to  the  directing  circle  BC  at  the  point  C. 

3d.  Divide  the  generating  circles  into  any  number  or  equal 
parts  as  i,  2,  3,  etc.,  and  set  off  the  length  of  these  divisions 
from  C  on  CB  as  e',  d',  c' ,  etc. 

4th.  From  A  the  center  of  the  directing  circle  draw  lines 


FIG.  67. 


FIG.  68. 


through  e',  d' ',  c',  etc.,  cutting  the  circles  of  centers  in  e,  d,  c, 
etc. 

5th.  From  each  of  these  latter  points  as  centers  describe 
arcs  tangent  to  the  directing  circle  CB. 

6th.  From  center  A  draw  arcs  through  the  points  of 
division  on  the  generating  circle,  cutting  the  arcs  of  the  gen- 
erating circles  in  their  several  positions  at  the  points  i',  2',  3', 
etc.  i,  2,  3,  etc.  These  will  be  points  in  the  two  curves. 

PROB.  25,  FIG.  68.  To  constrict  an  oval  the  width  AB  being 
given. 

i  st.  Draw  AB  and  CD  at  right  angles  to  each  other  in 
the  center  of  a  space  making  AB  equal  to  i\"  long. 


FREEHAND  LETTERING  AND  GEOMETRICAL  DRAWING    71 


2d.  With  E  as  center  and  EA  as  radius,  draw  the  semi- 
circle ACB  and  cutting  CD  in  F. 

3d.  From  A  and  B  draw  lines  through  F,  and  from  A  and 
J5  as  centers  and  AB  as  radius  draw  arcs  cutting  these  lines 
in  G  and  H. 

4th.  With  F  as  center  and  radius  FG  describe  the  arc  GH  to 
meet  the  arcs  AG  and  BE,  and  complete  the  curve  of  the  oval. 


K 


FIG.  70. 


PROB.  26,  FIG.  69.  Construct  the  Archimedes  spiral  of  one 
revolution. 

i st.  Describe  a  circle  using  the  widest  limit  of  the  spiral 
as  a  radius,  say  i|",  and  divide  the  circle  into  any  number  of 
equal  parts,  say  12. 

2d.  Divide  the  radius  into  the  same  number  of  equal  parts 
as  i  to  12. 

3d.  From  the  center  with  radius  12  i,  describe  an  arc 
cutting  the  radial  line  B  in  the  point  i'. 

4th.  From  the  center  continue  to  draw  arcs  from  points 
2,  3,  4,  etc.,  cutting  the  corresponding  radii  C,  D,  E,  etc., 
in  points  2',  3',  4',  etc.,  and  through  the  points  A,  i',  2',  3', 
etc.,  with  the  irregular  curve  draw  the  spiral. 

Fig.  70.  This  figure  shows  the  application  of  the  Archi- 
medes Spiral  in  the  heart-shaped  cam,  which  is  used  to  change 
rotary  motion  into  uniform  reciprocating  motion. 

PROB.  27,  FIG.  71.  Draw  an  arc  of  a  circle  tangent  to  two 
straight  lines  BC  and  CD  given  the  mid  position  G. 


72  MECHANICAL  DRAWING 

ist.  Draw  EC  i\"  long  f"  above  the  border  line  and  CD 
i\"  long  at  an  angle  of  120°  to  BC. 

2d.  Draw  CA  the  bisector  of  angle  BCD,  and  EF,  at  right 
angles  to  CA  through  the  point  G. 

3d.  Bisect  either  of  the  angles  BEF  or  EFD  this  bisector 
will  intersect  the  center  line  CA  at  A  the  center  of  the 
required  arc. 

4th.  From  A  draw  perpendiculars  Ai  and  A2,  and  with 
either  as  a  radius  and  A  as  center,  describe  an  arc  which 
will  be  tangent  to  the  lines  BC  and  CD  at  the  points  i  and  2. 


38.  Freehand  Lettering.  Plate  5  will  consist  of  the  same 
style  of  letters  drawn  in  Plates  i  and  3.  In  this  plate  they 
are  to  be  drawn  3  spaces,  2  spaces  and  i  space  high. 

i st.  About  15"  from  the  top  and  left-hand  edge  of  the 
cross-section  pad  begin  the  guide  lines  for  the  3  space  high 
letters.  These  guide  lines  should  be  fine,  narrow,  light  lines 
drawn  with  4H  pencil  sharpened  as  explained  in  Art.  7. 
The.  3  space  letters — that  is  3  spaces  high — should  not  be 
more  than  i  space  apart  and  the  slope  of  the  letters  should 
be  in  the  same  proportion  to  the  height  as  for  the  6  space 
high  letters,  namely  i^  spaces,  in  short,  all  dimensions  of 
the  3  space  high  letters  are  to  be  made  just  half  of  those  of 
the  6  space  high  letters. 

2d.  Draw  the  2  space  high  letters  using  guide  lines  as 
before  and  make  all  dimensions  and  slope  exactly  one-third 
of  the  6  space  high  letters.  For  the  vertical  spacing  of  the 
lines  of  lettering  in  this  plate,  see  Fig.  72. 


FREEHAND  LETTERING  AND   GEOMETRICAL  DRAWING    73 


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74  MECHANICAL  DRAWING 

3d.  In  drawing  the  i  space  high  letters  there  are  four  rules 
to  be  observed,  i.  Increase  the  slope  to  not  less  than  three- 
quarters  of  the  height.  This  is  necessary  because  the  small 
letters  do  not  seem  to  slope  as  much  as  the  large  letters  when 
the  slope  is  made  just  half  the  height.  2.  The  width  of  the 
small  letters  must  also  be  increased  because  wide  letters  i  space 
high  have  a  better  appearance  than  narrow  ones.  3.  Open 
letters,  that  is,  letters  like  E  and  F,  should  be  placed  close 
together  and  closed  letters  like  H  and  I  should  be  spaced 
farther  apart.  4.  Words  should  be  placed  2  spaces  apart  for 
this  size  of  letter.  In  Fig.  72  the  lettering  is  by  no  means 
perfect.  The  student  should  examine  each  letter  for  form, 
proportion  and  spacing  and  improve  upon  them  in  all  possible 
ways. 

4th.  When  all  the  letters  in  this  plate  have  been  properly 
pencilled  in,  they  should  be  inked  with  the  ball-pointed  pen. 
The  inked  lines  of  the  letters  should  be  of  medium  width  and 
drawn  smoothly  with  very  little  pressure  on  the  pen. 

PLATE  6.  This  plate  will  consist  of  the  numerals  as 
shown  in  Fig.  73,  viz.,  one  set  of  numbers  6  spaces  high,  one 
set  3  spaces  high,  one  set  2  spaces  high,  together  with  frac- 
tions and  i  space  high  numbers. 

i  st.  Locate  the  bottom  of  the  set  of  6  space  high  letters 
i  J"  from  the  top  of  the  sheet  .and  f  "  from  the  left-hand  end. 
Draw  the  guide  lines  as  indicated  and  pencil  in  the  numbers 
with  the  4H  pencil  sharpened  to  a  conical  point. 

2d.  Draw  the  set  of  3  space  high  numbers. 

Use  guide  lines  and  make  the  widths  in  the  same  pro- 
portion to  the  height  as  in  the  6  space  high  numbers. 

3d.  Draw  the  large  fractions,  making  the  numerators  and 
denominators  2  spaces  high  and  the  space  for  the  dividing 
line  i  square  high.  Use  guide  lines  and  proportions  as  above. 
Care  should  be  taken  to  obtain  the  proper  slope  for  the  whole 
fraction,  as  shown  in  the  figure. 

4th.  Draw  the  2  space  high  numbers  and  smaller  fractions. 
Guide  lines  should  be  used  for  all  numbers  2  spaces  high  and 
over. 


FREEHAND  LETTERING  AND  GEOMETRICAL  DRAWING   75 


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76  MECHANICAL  DRAWING 

The  i  space  high  numbers  should  be  drawn  without  guide 
lines.  The  2  and  i  space  numbers  are  to  be  inked  after  pen- 
cilling. The  larger  numbers  are  to  be  finished  in  pencil. 

PLATE. 7.  This  plate  is  to  consist  of  i  space  high  letters, 
all  capitals,  Gothic  style,  as  shown  in  Fig.  74. 

The  directions  given  for  drawing  the  small  letters  in  Plate 
5  will  also  apply  here.  Draw  carefully  in  pencil  first  and  then 
ink  in  with  the  ball-pointed  pen. 

PLATE  8.  This  plate  is  to  consist  of  lower  case  letters  6 
spaces  high  and  arranged  on  the  plate  as  shown  in  Fig.  75. 

This  style  of  letter  is  used  by  some  draftsmen  for  notes -on 
structural  drawings,  but  the  Gothic  style,  all  capitals  of  the 
same  height  is  the  most  popular.  Finish  in  pencil.  Ink 
title  only. 

PLATE  9  will  consist  of  lower  case  letters,   i   space  high. 

The  form  and  proportion  will  conform  to  the  form  and 
proportions  given  in  Plate  8. 

The  slope  of  the  letters  in  this  plate  should  be  about 
three-quarters  of  the  height.  Letter  plate  with  4.H  pencil 
and  when  approved,  ink  with  Gillott  pen  No.  303. 

PLATE  10  is  to  consist  of  Gothic  capitals,  i  space  high. 
Slope  not  less  than  three-quarters  of  the  height. 

Notice  the  extra  space  between  paragraphs. 

The  numbers  should  be  i|  times  higher  than  the  height 
of  the  letters.  On  all  occasions  when  letters  and  numbers 
are  combined  the  numbers  should  always  be  a  half  higher 
than  the  letters. 

This  being  the  last  plate  of  lettering  it  should  show  a 
maximum  of  improvement  over  preceding  plates.  Pencil  in 
with  4.H  and  ink  with  ball-point  No.  516.  The  lettering 
should  be  approved  by  the  instructor  before  inking. 


FREEHAND  LETTERING  AND  GEOMETRICAL  DRAWING   77 


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FREEHAND  LETTERING  AND  GEOMETRICAL  DRAWING    79 


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CHAPTER  IV 

ORTHOGRAPHIC  PROJECTION 

39.  Orthographic  Projection,  sometimes  called  Descriptive 
Geometry   and   sometimes   simply   Projection,    is   one   of   the 
divisions    of    descriptive    geometry;      the    other   divisions  are 
Spherical  Projection,  Isometric  Drawing,  Shades  and  Shadows, 
and  Linear  Perspective. 

In  this  course  we  will  take  up  only  a  sufficient  number  of 
the  essential  principles  of  Orthographic  Projection,  Isometric 
Drawing,  Shades,  Shadows  and  Shade  Lines,  to  enable  the 
student  to  make  a  correct  commercial  drawing  of  a  machine 
or  other  object. 

40.  Orthographic  Projection  is  the  science  and  the  art  of 
representing  objects  on  different  planes  at  right  angles  to  each 
other,  by  projecting  lines  from  the  point  of  sight  through  the 
principal  points  of  the  object  perpendicular  to  the  Planes  of 
Projection. 

There  are  usually  three  planes  of  projection  used,  viz.,  the 
horizontal  plane  or  H,  for  short,  the  vertical  plane  or  V,  and 
the  profile  plane  or  P.  Fig.  78. 

Auxiliary  planes  are  also  used.  These  may  be  parallel, 
oblique  or  at  right  angles  to  H  or  V  according  to  the  con- 
ditions of  the  problem. 

The  H  and  V  planes  intersect  one  another  at  right  angles 
in  the  line  of  intersection  or  ground  line  GL  and  form  four 
dihedral  angles. 

The  first  angle  is  above  H  and  in  front  of  V. 

The  second  angle  is  above  H  and  behind  V. 

The  third  angle  is  below  H  and  behind  V. 

The  fourth  angle  is  below  H  and  in  front  of  V. 

81 


82 


MECHANICAL  DRAWING 


41.  The  Profile  Plane  is  perpendicular  to  both  the  V  and 
H  planes  and  is  used  in  mechanical  drawing  to  obtain  end 
views  of  objects. 

Fig.  78  is  a  pictorial  view  of  V  and  H  together  with  the 
right-  and  left-hand  P  planes.  Fig.  79  is  an  orthographic  end 
or  profile  view  of  these  planes. 

When  viewing  the  planes  of  projection  the  observer  should 
be  stationed  so  that  he  is  looking  directly  into  the  ist  and 
4th  angles.  These  angles  then  will  be  in  front  of  V  nearest 


H 


FIG.  78. 


FIG.  79. 


the  observer  while  the  2d  and  3d  angles  are  behind  V  away 
from  the  observer. 

According  to  Article  40  objects  placed  in  space  in  any  of 
these  angles  may  be  projected  upon  the  V,  H,  and  P  planes 
by  passing  lines  through  their  principal  points  perpendicular 
to  the  planes  V,  H,  and  P,  respectively.  These  lines  will 
pierce  the  planes  of  projection  in  points  or  traces.  If  these 
points  are  connected  in  proper  sequence  by  lines,  an  ortho- 
graphic projection  of  the  object  will  be  had  on  the  three 
planes  of  projection. 


ORTHOGRAPHIC  PROJECTION 


83 


But  these  planes  are  at  right  angles  to  one  another  and 
the  three  views  are  also  at  right  angles  to  one  another, 
while  our  drawing  boards  and  drawing  papers  are  flat;  there- 
fore, the  planes  containing  the  projections  must  be  revolved 
into  the  flat  to  obtain  a  practical  working  drawing. 

41.  Revolution    of   the   Planes.     Let   the   horizontal  plane 
represent  the  drawing  board  and  paper  lying  in  a  horizontal 
position    on    the    drawing    table.     Then    if    the    V   plane    is 
revolved  about  the    G.L.    counter-clockwise "  until  it  coincides 
with   H,    the  V  projection    of    the    object   referred  to  above 
is  revolved  into  the  H  plane  or  the  plane  of  the  paper  either 
above  or  below  the  GL.     If  the  object  is  in  the  ist  angle  the  V 
projection  will  show  above  G.L.  after  revolution  and  the  H 
projection  will  remain  below.     The  Profile  Plane  should  be  re- 
volved so  that  the  P  projection  will  show  in  its  proper  quadrant 
after  revolution  according  to  the  angle  in  which  it  is  projected. 

42.  In  order  to  still  further  explain  the  use  of  the  planes 
of  projection,    with   regard    to   objects   placed   in   any   angle, 
let  us  suppose  a  truncated  pyramid  surrounded  by  imaginary 
planes  at  right  angles  to  each  other,  as  shown  by  Fig.  80. 


"  FIG.  80. 

With  a  little  attention  it  will  easily  be  discerned  that  the 
pyramid  is  situated  in  the  third  dihedral  angle,  and  that  in 
addition  to  the  V  and  H  planes,  we  have  passed  two  profile 
planes  at  right  angles  to  the  V  and  H  planes,  one  at  the 
right  hand  and  one  at  the  left. 

When  the  pyramid  is  viewed  orthographically  through 
each  of  the  surrounding  planes,  four  separate  views  are  had, 
exactly  as  shown  by  the  projections  on  the  opposite  planes, 
viz.,  a  Front  View,  Elevation  or  Vertical  Projection  at  F,  a 


84 


MECHANICAL  DRAWING 


Right-hand  View,  Right-end  Elevation  or  Right  Profile  Pro- 
jection at  R.  A  Left-hand  View,  Left-end  Elevation,  or  Left 
Profile  Projection  at  L. 

A  Top  View,  Plan  or  Horizontal  Projection  at  P. 

If  we  now  consider  the  V  plane  and  the  right  and  left  P 
planes  to  be  revolved  toward  the  beholder  while  looking  down 
on  H  until  they  coincide,  using  the  front  intersecting  lines 
as  axes,  the  projections  of  the  pyramid  will  be  seen,  as 
shown  in  Fig.  81,  which,  when  the  imaginary  planes  and  pro- 


\     / 


F 


H 


FIG.  81. 

jecting  lines  have  been  removed,  will  be  an  orthographic 
projection  or  true  drawing  of  the  truncated  pyramid. 

43.  To  Illustrate  Projections  in  the  Different  Angles. 
Let  Fig.  82  be  a  pictorial  view  of  the  intersecting  planes  of 
projection  V,  H,  and  P,  and  B  a  rectangular  block  situated 
in  space  in  the  ist  angle.  The  observer  in  front  looking 
toward  the  V  plane  can  imagine  parallel  lines  projected 
through  the  four  corners  of  the  nearest  face  of  the  block  and 
prolonged  toward  V  and  perpendicular  to  it  until  these  lines 
pierce  V  in  four  points  called  the  traces  of  the  lines.  If 
these  points  are  joined  with  straight  lines  parallel  to  each 
other,  there  will  be  formed  on  the  V  plane  a  V  projection 
of  the  block  in  the  ist  angle. 

In  a  similar  manner  the  observer  viewing  the  block  from 
above  may  project  the  top  view  of  the  block  upon  the  H 


ORTHOGRAPHIC  PROJECTION 


85 


plane  determining  the  H  projection  of  the  block  in  the  ist 
angle  seen  at  H. 

The  P  projection  may  also  be  found  in  a  similar  manner 
by  viewing  the  block  from  the  right  and  projecting  that  view 
of  the  block  upon  P. 

Authorities  differ  as  to  the  proper  way  of  viewing  the 
object  when  projecting  on  the  profile  plane  from  the  ist 
angle.  Some  hold  that  in  teaching  descriptive  geometry,  the 
object  should  be  viewed  from  the  right  in  all  angles  when 


1st 

p 


H 


FIG.  82. 


FIG.  83. 


projecting  on  the  profile  plane.  It  works  all  right  in  the 
ist  angle  if  the  P  line  is  placed  far  enough  to  the  right  of  the 
V  projection  so  that  the  profile  projection  when  revolved 
(away  from  the  observer)  will  not  overlap  the  V  projection. 
It  places  .the  right  end  view  of  the  object  directly  beside  the 
right  end  of  the  V  projection,  as  seen  in  Fig.  83.  But  the 
plan  or  top  view  of  the  object  remains  below  the  V  projec- 
tion after  the  V  plane  has  been  revolved  into  the  H  plane  or 
plane  of  the  drawing  board. 

Others  recommend  that  an  object  in  the  ist  angle  should 
be  viewed  from  the  left  when  projecting  on  the  P  plane  and 
from  the  right  when  viewing  an  object  in  the  3d  angle. 


MECHANICAL  DRAWING 


What  has  already  been  said  about  projection  in  the  3d 
angle  shows  that  it  is  the  proper  angle  to  use  in  projecting 
working  drawings. 

In  Fig.  83  is  shown  the  three  views  of  the  object  on  the 
flat  after  the  P  plane  has  been  revolved  into  V  and  the  V 
plane  into  H. 

Fig.  84  shows  the  same  block  situated  in  space  in  the  3d 
angle,  below  H  and  behind  V.  The  observer  is  located  as 


FIG.  84. 


FIG.  85. 


before  in  front  of  and  looking  toward  the  V  plane.  Parallel 
lines  perpendicular  to  V  are  conceived  to  pass  through  the 
four  corners  of  the  front  face  of  the  block  and  where  these 
lines  pierce  the  V  plane  will  be  four  points  of  the  V  pro- 
jection of  the  block  on  the  V  plane.  When  these  points  are 
joined  by  parallel  straight  lines  the  V  projection  of  the  block 
will  be  complete.  The  plan  or  H  projection  is  found  in  a 
similar  manner  looking  from  above  toward  the  H  plane. 
The  P  projection  is  found  by  looking  toward  the  right-hand 
end  of  the  block  through  the  P  plane,  as  shown.  Fig.  85 
shows  the  drawing  of  the  block  on  the  flat  in  the  3d  angle 


ORTHOGRAPHIC  PROJECTION 


87 


after  the  planes  have  been  revolved  around  the  axes  G.L. 
and  P  as  explained  in  the  projection  in  the  ist  angle. 

Projections  in  the  2d  and  4th  angles  are  seldom  used 
except  in  solving  problems  in  descriptive  geometry.  The 
method  of  projection,  however,  is  the  same  as  given  for  the 
ist  and  3d. 

Commercial  engineering  drawings  are  made  almost  entirely 
in  the  3d  angle.  The  3d  angle  is  preferable  for  various 
reasons.  Take,  for  example,  the  side  view  of  a  locomotive 
on  the  tract.  In  a  drawing  this  would  represent  the  vertical 
projection  and  in  3d  angle  projection  the  profile  view  of  the 
front  or  smoke-box  end  would  be  placed  directly  beside 
itself  to  the  right  of  the  front  and  whereas  in  ist  angle  pro- 
jection the  same  front-end  view  would  be  projected  across 
the  vertical  projection  and  placed  at  the  left.  See  Fig.  86. 


FIG.  86. 


QUESTIONS  ON  CHAPTER  IV 

1.  What  is  orthographic  projection?.     Art.  40. 

2.  What  are  the  principal  planes  of  projection? 

3.  What  other  planes  are  sometimes  used? 

4.  What  angles  are  formed  by  the  H  and  V  planes?     Give  names  and 
how  numbered. 

5.  Where  is  the  first  angle  located  with  reference  to  the  H  and  V  planes? 


88  MECHANICAL  DRAWING 

6.  Where  is  the  second  angle  located  with  reference  to  the  H  and  V 
planes? 

7.  Where  is  the  third  angle  located  with  reference  to  .the  H  and  V  planes? 

8.  Where  is  the  fourth  angle  located  with  reference  to  the  H  and  V 
planes? 

9.  Explain  how  objects  in  space  in  any  of  these  angles  are  projected 
upon  the  planes  of  projection. 

10.  What  is  called  the  vertical  projection? 

11.  What  is  the  horizontal  projection? 

12.  What  is  the  profile  projection? 

13.  What  projection  is  called  the  front  view  or  elevation? 

14.  What  projection  is  called  the  top  view  or  plan? 

15.  What  projection  is  called  the  end  view  or  end  elevation? 

1 6.  How  are  the  planes  revolved  to  obtain  the  drawings  on  the  flat? 

17.  How  should  the  profile  plane  be  revolved? 

1 8.  What  angle  does  the  projection  lines  make  with  the  planes  of  pro- 
jection? 

19.  What  is  the  name  of  the  line  in  which  the  H  and  V  planes  intersect? 

20.  What  angle  is  mostly  used  in  projecting  engineering  drawings? 

21.  Explain  why  one  angle  is  better  than  another  in  making  working 
drawings. 


CHAPTER  V 

THE  REPRESENTATION  OF  POINTS  AND  LINES 

44.  Points.     Having  well  in  mind  the  representation  of  the 
Planes  of  Projection  at  right  angles  to  each  other  forming  the 
four   dihedral   angles   as   described   in   the   previous   chapter; 
it  is  easy  for  the  student   to   conceive  a  point  situated  in 
space  in  any  one  of  these  angles  and  to  project  it  upon  the 
V  and  H  planes  by  passing  lines  through  the  point  perpen- 
dicular to  H  and  V.     The  points  in  which  these  perpendicular 
lines  pierce  the  V  and    H  planes  are  the  vertical  and  hori- 
zontal projections  of   the   point  in   space,   and  when   the    V 
plane  has  been  revolved  away  from  the  observer  to  coincide 
with  H  the  vertical  and  horizontal  projections  of  the  point  will 
lie  in  a  straight  line  perpendicular  to   G.L. 

45.  Notation  of  Points.     Capital   letters  will  be  used   to 
designate  points  in  space  and  lower  case  letters  for  the  pro- 
jections of  points.    The  vertical  projection  to  have  a  prime 
placed   to   the   right   and   above    the    "point's"  letter.    See 
Fig.  87. 

A  represents  the  given  point  in  space  in  the  first  angle, 
a'  its  vertical  projection,  a  its  horizontal  projection  and  a'p  its 
profile  projection. 

46.  Location  of  Points.     Points  are  located  with  reference 
to  their  distance  from  the  planes  of  projection.      For  example: 
4(2"+iJ"-i")  means  that  the  point  A  is  2"  from  the  left- 
hand  border  line,   if"  above  G.L.  and  i"  below  G.L.  or  in 
other  words  the  point  A  is  ij"  above  H  and  i"  in  front  of  V. 

The  first  term  in  the  parenthesis  gives  the  distance  from 
the  left-hand  border  line  measured  along  the  G.L. 

The  second  term  is  always  the  V  projection  whether  plus 

89 


90 


MECHANICAL  DRAWING 


or  minus.  If  plus  it  is  laid  up  on  a  line  perpendicular  to 
and  above  G.L.  If  minus  it  is  laid  off  on  a  line  perpendicular 
to  and  below  G.L. 

The  third  term  is  always  the  H  projection  whether  plus 
or  minus.  If  plus  it  is  located  above  and  if  minus,  below,  as 
before. 

A  point  located  in  the  vertical  plane  will  have  its  H  pro- 
jection in  G.L.  A  point  located  in  the  horizontal  plane  will 
have  its  V  projection  in  G.L. 

Example:  5(3,0+1)  means  that  a  point  on  G.L.  3"  from 
the  left-hand  border  line  is  the  V  projection  of  the  point  B 


FIG.  87. 


and  on  a  line  through  that  point  perpendicular  to  G.L.  and 
i"  above  it  is  located  the  H  projection  of  the  same  point, 
3d  angle  projection. 

47.  Projection  of  Points  on  the  V,  H  and  P  Planes. 
The  projection  of  a  point  in  the  first  angle  is  illustrated  in 
Fig.  87.  The  point  A  is  shown  in  space  above  H  and  in 
front  of  V  and  when  projected  on  the  V  plane  at  a'  and  the 
V  plane  revolved  away  from  the  observer  until  it  coincides 
with  the  H  plane,  then  the  point  A  is  shown  in  vertical  pro- 
jection at  a'i,  above  the  G.L.  The  H  projection  remains  at  a' 
below  the  G.L. 


THE  REPRESENTATION  OF  POINTS  AND  LINES 


•91 


The  three  projections  of  A  on  the  flat  are  shown  in  Fig.  88. 

Notice  that  the  P  projection  av'  is  at  the  left  of  the  P 
line  which  is  placed  at  a  distance  from  the  V  projection  suit- 
able to  enable  the  P  projection  to  be  revolved  into  the  V 
plane  without  interfering  with  the  V  projection. 

The  projection  of  a  point  lying  in  H  in  front  of  V  will 
have  its  V  projection  in  the  G.L.  and  its  H  projection  on  a 
line  drawn  through  the  V  projection  perpendicular  to  G.L. 
at  a  distance  from  G.L.  equal  to  the  distance  of  the  point 
from  the  V  plane.  The  P  projection  will  be  in  G.L.  to  the 
left  of  P  since  the  point  is  in  front  of  V  and  viewed  from 
the  right.  See  Fig.  88. 


G 


1st                        In  H  in  front  of  V          In  V  above  H 

P 

P 

P 

a' 

a'P 

a\ 

a'P 

a 

/ 

a 

a     i 

,  \ 

. 

\ 

FIG.  88. 


A  point  in  V  above  H  has  its  H  projection  in  G.L.  and 
its  P  projection  in  the  P  line  since  the  P  line  is  the  end 
view  of  the  V  plane.  See  Fig.  88. 

A  point  in  space  in  the  3d  angle  at  A,  Fig.  89,  viewed 
from  the  front  through  the  V  plane  has  its  V  projection 
below  the  G.L.  and  viewed  from  above  its  plan  or  H  pro- 
jection above  G.L.  Its  P  projection  will  revolve  to  the  right 
of  the  P  line  below  G.L.  See  Fig.  89. 

A  point  in  space  in  the  2d  angle  at  A,  Fig.  90,  viewed 
from  the  front  through  V  has  its  V  projection  above  G.L.  and 
viewed  from  above  its  H  projection  also  falls  above  G.L. 


MECHANICAL  DRAWING 


Its  P  projection  viewed  from  the  right  revolves  to  the  right 
of  the  P  line  above  G.L.  into  the  2d  quadrant.  See  Fig.  91 
for  the  projections  on  the  flat. 


is 


a/ 


\ 


FIG.  89. 

The  projection  of  a  point  in  space  in  the  4th  angle  is 
illustrated  in  Fig.  92.  A  is  the  point  in  space.  When  viewed 
from  the  front  its  V  projection  falls  on  the  V  plane  below 
G.L.  and  its  H  projection  viewed  from  above  falls  on  the 
H  plane  below  G.L. 


51 


G 


FIG.  90. 


FIG.  91. 


The  P  projection  of  a  point  in  the  4th  angle  viewed  from 
the  right  shows  the  point  to  the  left  of  the  P  line  in  the  4th 
quadrant  when  revolved  into  the  flat.  See  Fig.  91. 

48.  Plate  ii.    This  plate  will  consist  of  the  projection  of 


THE  REPRESENTATION  OF  POINTS  AND  LINES 


93 


points,  lines  and  planes.     Lay  out  the  plate  as  shown  in  Fig.  93, 
dividing  the  space  inside  the  border  line  into  16  equal  spaces. 

4th 
P 


1 

/ 

V  /r> 

D 

x* 

ft 

/ 

7 

/»    » 

/ 

A 

A 

FIG.  92. 


There  will  be  15  problems.  A  title  is  to  be  carefully 
lettered  in  the  i6th  space.  Use  the  standard  title  shown  at 
Fig-  35  and  make  the  name  of  this  plate  "  Projections." 

All  drawings  are  to  be  made  first  in  fine,  narrow  lines 
with  the  6H  pencil  sharpened  as  described  in  Art.  4. 


0 

G 
G 
G 

a' 
<-2^-> 

1 

% 

< 

k'^d  T 

a 

JL 

1 

^^•"H 
t 

L 
TITLE 

FIG.  93. 

As   soon   as   the   projection   of   a   point   is   located   mark 
it  with  its  proper  letter  as  directed  in  Art.  55,  and  designate 


94  MECHANICAL  DRAWING 

the  angle  in  which  it  is  projected  in  neat  lettering  above 
the  projection  of  the  point.  See  Fig.  88,  page  91. 

When  all  the  problems  in  Plate  n  have  been  drawn  in 
fine  lines  and  approved  (the  problems  should  be  submitted 
one  by  one  for  examination),  all  the  given  and  required  lines 
should  then  be  strengthened  with  the  4.H  pencil,  as  described 
in  Art.  35. 

Projection  lines  must  be  made  very  narrow  and  unbroken. 

Traces  of  planes  will  be  shown  by  a  long  dash  and  two 
short  dashes  alternately.  The  short  dashes  about  f"  long 
and  jV  apart  thus: 


Width  about 


PROB.  28.     Draw  the  V,  H  and  P  projections  of  the  following 
points.    Locate  the  P  line  to  suit. 


The  projections  of  these  points  are  to  be  drawn  in  the  first 
division  on  the  plate  in  the  upper  left-hand  corner. 

PROB.  29.  Draw  the  V,  H  and  P  projections  of  the  following 
points: 


49.  Projection  of  Lines.  The  projections  of  two  points 
of  a  straight  line  determine  the  projections  of  the  line. 

The  projections  of  a  line  are  the  traces  of  the  projecting 
planes  of  the  line.  The  projecting  planes  are  perpendicular 
to  H  and  F,  respectively,  and  intersect  each  other  in  the  line 
itself  and  determine  it  in  space. 

In  Fig  94,  Abf  and  Ba  are  two  projecting  planes  at  right 
angles  to  each  other  and  perpendicular  to  V  and  H,  respec- 
tively. ab  is  the  H  trace  of  the  plane  Ba  and  also  the  hor- 
izontal projection  of  the  line  AB.  a'b'  is  the  trace  of  the 
plane  A  /  and  also  the  vertical  projection  of  the  line  AB. 

AB  is  the  line  of  intersection  between  the  two  projecting 
planes  and  also  the  line  itself  in  space, 


THE  REPRESENTATION  OF  POINTS  AND  LINES 


95 


When  given  the  locations  of  two  points  as  A  and  B  of  the 
line  AB  with  reference  to  the  planes  of  projection,  proceed 
toi  draw  their  projections  exactly  as  explained  for  the  pro- 
jection of  points,  and  then  draw  a  straight  line  from  the  V 
projection  of  A  to  the  V  projection  of  B  as  a'b' ',  Fig.  95, 
then  a'b'  is  the  V  projection  of  the  line  AB.  Draw  the  H 
projections  of  the  points  A  and  B  as  a  and  b  and  join  a  and 
b  with  a  straight  line,  then  0,  b  is  the  H  projection  of  the 
line  AB.  Fig.  95  shows  the  drawing  on  the  flat. 

The  profile  projection  is  found  in  the  same  manner  as  is 
used  in  finding  the  profile  of  points.  See  the  profile  pro- 


FIG.  94. 


jection  of  point  A  in  the  ist  angle  Fig.  88.  A  line  is  drawn 
through  a  parallel  to  G.L.  to  intersect  P.  The  point  when 
it  intersects  P  is  revolved  into  G.L.  and  a  line  erected  at 
that  point  to  meet  a  horizontal  line  through  a'  at  ap'  the  P 
projection  of  the  point  A  in  the  ist  angle  when  viewed  from 
the  right.  The  method  of  drawing  the  P  projection  of  the 
points  A  and  B  in  Fig.  95  amounts  to  the  same  thing.  The 
angle  between  the  P  line  and  G.L.  below  G.L.  is  bisected 
by  a  45°  line  and  horizontal  lines  drawn  through  a  and  b 
to  meet  it.  At  the  points  where  these  lines  meet  the  bi- 
sector, erect  perpendiculars  to  meet  horizontals  through  a' 
and  b'  in  the  P  projections  of  A  and  B  in  the  ist  angle,  as 
before,  when  viewed  from  the  right, 


96  MECHANICAL  DRAWING 

50.  If  a  line  is  parallel  to  H  its  V  projection  is  parallel 
to  G.L.  Fig.  960. 

If  a  line  is  parallel  to  V  its  H  projection  is  parallel  to 
G.L.  Fig.  966. 

If  a  line  is  oblique  to  H  and  V  its  projections  are  inclined 
to  G.L.  Fig.  g6c. 

If  a  line  is  perpendicular  to  H  its  projection  on  that  plane 
will  be  a  point  and  its  V  projection  will  be  perpendicular  to 
G.L.  Fig.  96d. 

If  a  line  is  oblique  to  H  it  will  pierce  H  when  pro- 
longed. 

The  point  where  the  line  pierces  H  is  called  the  piercing 
point,  sometimes  called  the  trace  of  the  line.  Fig.  $6e. 


t 
a        ^b          c 

/           e                        ' 

/  / 

g 

/  —  \  •   —        \ 

FIG.  96. 

If  a  line  is  parallel  to  both  H  and  V  both  of  its  projec- 
jections  are  parallel  to  G.L.  Fig.  967. 

If  a  line  lies  in  H  its  H  projection  is  the  line  itself  and 
its  V  projection  is  in  the  G.L.  Fig.  96^. 

If  a  line  lies  in  P  its  V  projection  will  be  in  the  V  trace 
of  the  P  plane  and  its  H  projection  will  lie  in  the  H  trace 
of  the  P  plane.  Fig.  g6h. 

It  has  been  shown  (Art.  49)  that  the  projections  of  two 
points  of  a  line  determine  the  projections  of  the  line.  Two 
points  are  also  necessary  to  determine  a  line  in  space  as  to 
its  length  and  direction  but  one  point  and  the  direction  of 
the  line  will  also  locate  it  in  space. 

51.  If  two  lines  intersect  in  space  their  projections  will 
intersect  in  a  point  on  a  line  perpendicular  to  G.L.  Fig.  97. 


THE  REPRESENTATION  OF  POINTS  AND  LINES 


97 


Lines  which  do  not  intersect  in  space  may  intersect  in 
projection  but  not  in  the  same  straight  line  perpendicular 
to  GX.  Fig.  98. 


d' 


FIG.  97. 


FIG.  98. 


If  two  lines  are  parallel  to  each  other  in  space,  their  pro- 
jections will  be  parallel  to  each  other  on  the  same  plane. 
Fig.  99. 


FIG.  99. 


FIG.  100. 


Lines  oblique  to  V  and  H  do  not  show  their  true  lengths. 

52.  To  find  the  true  length  of  a  straight  line  obi  que  to  both 
plan  3  3  of  projection.  a',  bf  and  ab,  Fig.  100,  are  the  pro- 
jection of  a  line  in  space  oblique  to  V  and  H.  Its  true 
length  may  be  found  ist  by  revolving  parallel  to  V  or  H, 
2d  by  revolving  into  H  or  V. 

To  revolve  parallel  to  H.  Take  point  b'  as  center  and 
b'a'  as  radius  and  revolve  the  line  a'bf  until  it  is  parallel  to 


98 


MECHANICAL  DRAWING 


G.L.  at  a'ib'.  During  revolution  the  point  a  remains  at  the 
same  distance  from  V,  therefore,  the  projection  of  the  arc 
a' a' i,  will  be  a  straight  line  parallel  to  G.L.  drawn  through 
the  point  a  to  a\  which  is  the  H  projection  of  a\ '.  Join 
a\b  with  a  broken  line.  It  is  the  true  length  of  the  line  AB. 

To  revolve  into   H.     Fig.   101. 

At  a  and  b  erect  perpendiculars  to  ab.  At  a  lay  off  the 
distance  aa\  equal  to  the  distance  that  a'  is  above  G.L.  At 
b  lay  off  the  distance  bb\  equal  to  the  distance  that  b'  is 
above  G.L.  At  b  lay  off  the  distance  bbi  equal  to  the  dis- 


FIG.  102. 


tance  that  b'  is  above  G.L.  Draw  a\b\  in  a  broken  line.  It 
is  the  true  length  of  the  line  AB. 

53.  To  Find  where  a  Straight  Line  Pierces  the  Principal 
Planes  of  Projection.  A  straight  line  in  space  oblique  to  the 
planes  of  projection  will,  if  produced,  pierce  each  of  them 
in  a  point  and  since  the  piercing  point  lies  in  the  plane  its 
other  projection  will  lie  in  the  G.L. 

For  example:  a'b',  Fig.  102,  is  the  V  projection  of  a 
straight  line  in  space  oblique  to  H.  Extend  a'b'  to  meet  G.L. 
at  p1  erect  a  perpendicular  to  meet  the  extended  H  projection 
of  AB  at  the  point  p. 

The  point  p  is  the  H  piercing  point  of  the  line  AB. 
The  V  piercing  point  is  found  by  erecting  a  perpendicular 


THE  REPRESENTATION  OF  POINTS  AND  LINES          99 

at  the  point  0  (where  the   H  projection  of  AB  meets  G.L.) 
to  meet  the  V  projection. 

PROB.  30.     Draw  the  V,  H  and  P  projections  of  the  following 
lines.    Locate  the  P  line  to  suit. 


and 

PROB.  31. 

and 

PROB.  32. 

and 

PROB.  33.    .Dra^  /^e  #  projections  of  the  two  lines 
and 


intersecting  in  space,  see  Art.  51. 

PROB.  34.     Assume  the  H  projections  of  two  lines  parallel  to 
each  other  in  space  in  the  first  angle  and  draw  the  V  projections. 

PROB.  35.    Find  the  V  and  H  piercing  points  of  the  lines 


and 


CHAPTER  VI 

REPRESENTATION  OF  PLANES 

54.  Representation  of  Planes.  Many  other  planes  besides 
H  V  and  P  may  be  used  in  projection.  Such  planes  are 
shown  by  their  traces  on  the  principal  planes  of  projection. 


FIG.  103. 

Fig.    103   gives   a  pictorial  view  of  an   oblique  plane   T 
intersecting  H   and  V.     Tt'  is  the  V  trace  of  the    plane  or 

100 


REPRESENTATION 'OF 'PL^OT^        *>>;  >1    \  ;X01 

in  other  words  it  is  the  line  in  which  the  oblique  plane  pene- 
trates or  intersects  V.  Tt  is  its  H  trace  or  the  line  in 
which  the  oblique  plane  T  intersects  the  H  plane.  The 
orthographic  drawing  of  the  traces  of  the  plane  is  shown  a^ 
the  right  in  Fig.  103. 

Given  two  traces  of  a  plane  the  plane  is  completely 
determined. 

55.  Location  of  Planes.  Since  planes  are  determined  by 
their  traces  it  is  sufficient  to  give  the  location  of  the  traces 
with  reference  to  H  and  V  to  completely  determine  the  plane. 

The  traces  of  all  oblique  planes  must  meet  at  G.L.  This 
point  is  noted  with  a  capital  letter  as  T  in  Fig.  103,  and  the 
plane  is  known  as  the  plane  T. 

Traces  of  planes  are  located  in  a  similar  manner  to  that 
used  in  locating  points,  for  example: 


means  that  the  V  trace  of  the  plane  T  has  its  point  t' 
located  i"  from  the  left-hand  border  line  and  ij"  above 
G.L.  and  its  point  /  i"  from  the  left-hand  border  line  and 
2"  below  G.L.  while  the  point  of  intersection  of  the  two 
traces  on  G.L.  is  3"  from  the  left-hand  border  line.  See 
Fig.  93,  Art.  48. 

Note  that  in  the  first  parenthesis  the  ist  figure  is  the  dis- 
tance from  the  left  border  line  to  the  projection  line  of  a 
point  on  the  V  trace.  The  2d  term,  viz.,  "  +  i§"  (or  what- 
ever the  value  may  be)  is  always  the  V  projection  of  a  point 
on  the  V  trace  whether  plus  or  minus. 

The  figure  between  the  parenthesis  is  always  the  dis- 
tance of  the  meeting  point  of  the  two  traces  on  G.L.  from 
the  border  line. 

In  the  second  parenthesis  the  first  figure  is  the  distance 
from  the  left-hand  border  line  to  the  projection  line  of  a 
point  on  its  H  trace  as  /.  The  second  term,  viz.,  "  —  2"  is 
the  distance  that  the  point  /  on  the  H  trace  is  from  G.L. 

56.  Planes.  Planes  may  be  determined  in  space  by  three 
points  not  in  the  same  straight  line,  by  two  intersecting  lines, 


102  MECHANICAL  DRAWING 


two  parallel  lines,  or  by  one  point  and  a  straight  line.  Planes 
extend  indefinitely  so  that  they  intersect  one  or  both  of 
the  planes  of  projection. 

The  lines  in  which  a  plane  intersects  the  planes  of  pro- 
jection are  called  the  traces  of  the  plane.  These  trace  lines 
may  be  made  of  long  dashes  and  two  short  dashes  alternately, 
as  shown  in  Fig.  104. 

To  find  the  traces  of  a  plane  given  by  three  points  A,  B 
and  C.  Fig.  104, 


FIG.  104. 

Draw  through  any  two  of  the  points  a  straight  line  as  AC 
and  produce  it  to  pierce  H  at  D  and  V  at  E.  d  and  e'  are 
points  in  the  horizontal  and  vertical  traces  respectively. 
Draw  through  the  remaining  point  B  a  straight  line  to  inter- 
sect DE  in  any  point  F  and  produce  BF  to  pierce  H  and 
V  at  G  and  H.  g  is  a  second  point  in  the  horizontal  and  hf 
a  second  point  in  the  vertical  trace  of  the  plane  S. 

PROB.  36.    Draw  the  traces  of  the  plane  given  by  three  points 


57.  To  Pass  a  Plane  through  Two  Intersecting  Straight 
Lines.  Find  the  V  and  H  piercing  points  of  the  lines.  They 
will  be  points  in  the  traces  of  the  plane.  In  case  the  lines 
do  not  pierce  the  planes  of  projection  within  the  limits  of 
the  drawing,  connect  a  point  on  each  with  a  straight  line  and 
find  its  V  and  H  piercing  points.  Another  piercing  point 
found  in  a  similar  way  will  determine  the  plane. 

The  same  method  will  apply  in  passing  a  plane  through 


REPRESENTATION  OF  PLANES 


103 


two  parallel  straight  lines  or  through  a  point  and  a  straight 
line. 

PROB.  37.  Assume  the  V  and  H  projections  of  two  lines  inter- 
secting each  other  in  space  and  draw  the  traces  of  the  plane  containing 
them. 

58.  Given  the  traces  of  two  planes  to  find  the  line  of  inter- 
section between  them. 

The  point  of  intersection  A,  Fig.  105,  of  the  two  vertical 
traces  is  one  point  in  the  required  line.  The  point  of  inter- 
section B  of  the  horizontal  traces  is  another.  Join  these  two 
points  with  a  straight  line.  It  is  the  required  line  of  inter- 
section. 


FIG.  105. 


FIG.  106. 


59.  To  Find  the  Line  of  Intersection  of  Two  Planes  whose 
Traces  do  not  Intersect  within  the  Specified  Limits.  Pass 
two  planes  parallel  to  H.  These  auxiliary  planes  cut  from 
the  given  planes  straight  lines  parallel  to  their  horizontal 
traces. 

T  and  U,  Fig.  106,  are  the  traces  of  the  auxiliary  planes 
parallel  to  H.  ab  and  a'b' ,  cd  and  c'd'  are  the  projections 
of  the  lines  cut  from  the  planes  R  and  S.  Draw  a  line 
through  db  and  d'b' .  These  lines  are  the  horizontal  and  ver- 
tical projections  of  the  line  of  intersection  between  the  two 
planes  R  and  S.. 


104 


MECHANICAL  DRAWING 


PROB.  37.     Find  the  line  of  intersection  between  the  planes 
r(2"  +  if")f(4"-i)     and    S(2i"+iJ")3f"(2i"-ii"). 

PROB.  38.  Find  the  line  of  intersection  between  the  following 
planes  whose  traces  do  not  intersect: 

E7(2"  +  if")i(il"-i    and    F(3  +  i|)4(2f"-i). 

60.  To  Project  a  Given  Straight  Line  on  a  Given  Oblique 
Plane.  T  is  the  given  plane  and  AB  the  given  straight  line, 
Fig.  107. 


FIG.  107. 


FIG.  i 08. 


Assume  two  points  on  the  line,  say,  A  and  B,  and  through 
them  draw  lines  perpendicular  to  the  given  plane.  They  will 
be  perpendicular  to  the  traces  of  the  given  plane.  Find  their 
piercing  points  and  join  them  with  a  straight  line,  as  shown. 
aibia'ib'i  are  the  projections  of  the  line  on  the  plane. 

PROB.  39.  Project  the  HneA(%+%-$),  B(i%  +  i  —  i$)  on  the 
plane  ^2^+1(1)2^-1^). 

61.  To  Pass  a  Plane  through  a  Given  Point  Perpendicular 
to  a  Given  Straight  Line.  Through  the  point  C,  Fig. 


REPRESENTATION  OF  PLANES 


105 


draw  a  line  perpendicular  to  ab  and  parallel  to  H  and  find 
its  piercing  point  O.  Through  0  draw  the  traces  of  the  re- 
quired plane  perpendicular  to  the  line  AB. 

PROB.  40.     Pass  a  plane  through  the  point  A(i  —  if+i  per- 
pendicular to  the  line  C(iJ+i|-|),  #(3+5- ii). 

62.  To  Pass  a  Plane  Parallel  to  a  Given  Plane  at  a  Given 
Distance  from  it.     T,  Fig.  109,  is  the  given  plane.     Pass  a 
plane   R  perpendicular   to   T  and   revolve   it  into    H,    thus: 
Erect   a  perpendicular  at  R  and  lay  off  Rr'i  equal  to  Rr'. 


R 


FIG.  109. 


Join  a  and  r'\.  It  is  a  line  cut  from  the  plane  T  revolved 
into  H.  Perpendicular  to  this  line  lay  off  the  given  distance 
ab  equal  to  x.  Through  b  draw  a  line  parallel  to  ar\  cutting 
rR  in  the  point  c.  Through  c  draw  the  H  trace  of  the 
required  plan  5  parallel  to  Tt.  Draw  the  V  trace  Ssf  par- 
allel to  Tt' .  Angle  6  is  the  angle  which  the  plane  T  makes 
with  H. 

PROB.  41.  Draw  the  traces  of  a  plane  parallel  to  plane 
?Xi+if)3(£-i})  and  J"  from  it.  Measure  the  angle  the 
required  plane  makes  with  V. 

63.  Given  the  Traces  of  Two  Oblique  Planes  to  Measure 
the  Angle  between  Them. 


106  MECHANICAL  DRAWING 

i st.  Find  the  line  of  intersection  between  the  given  planes 
5  and  T,  Fig.  no. 

2d.  Pass  a  vertical  projecting  plane  perpendicular  to  the 
line  of  intersection  r'r';  is  its  V  trace.  This  auxiliary  plane 
will  cut  from  the  given  planes  two  straight  lines  which  form  a 
triangle  with  a'b'  as  its  base  and  the  point  c'  on  the  line 
of  intersection  its  vertex. 

3d.  Revolve  the  point  c'  around  the  line  r'r'  into  V  at 
Ci  join  c\  and  the  points  a'b'  with  straight  lines. 


The  angle  9  contained  between  them  is  the  angle  required. 

To  obtain  the  distance  c\  from  c',  revolve  the  line  of  inter- 
section into  V,  by  erecting  a  perpendicular  at  d'  and  laying  off 
the  distance  d'd\ ',  equal  to  d'd.  Draw  d\e' .  It  is  the  re- 
volved position  of  the  line  of  intersection.  Draw  c'c"  perpen- 
dicular to  die'.  It  is  the  distance  required. 

PROB.  42.  Find  the  angle  between  the  planes  S(iJ-f  iJ)J 
(if-ii),  and  7^(2  +  4)3(2!- 1|).  Also  find  the  angle  which  T 
makes  with  H. 


REPRESENTATION  OF  PLANES 


107 


64.  To  Find  the  Shortest  Distance  between  Two  Given 
Straight  Lines. 

Let  AB  and  CD,  Fig.  in,  be  the  two  given  straight  lines. 

ist.  Pass  a  plane  T  through  CD  parallel  to  AB. 

2d.  Project  the  line  AB  on  this  plane  (Art.  60)  thus: 
Through  any  point  on  AB,  as  H,  draw  a  line  perpendicular 
to  the  traces  of  T  and  find  its  piercing  point  on  plane  T  at  E. 
This  is  one  point  in  the  projection  of  AB  on  plane  T. 

3d.  Draw  through  E  the  line  EF  parallel  to  AB.  It  will 
intersect  CD,  which  is  also  lying  in  plane  T  in  the  point  F. 


FIG.  in. 


4th.  Draw  through  F  the  line  FG  perpendicular  to  the 
plane  T.  It  is  perpendicular  to  both  lines  and  is,  therefore, 
the  shortest  distance  between  them.  The  true  length  of  FG 
may  be  found  by  Art  52. 

PROB.  42.  Measure  the  shortest  distance  between  the 
straight  lines  4(f+iJ-o),  Bfci+o-iJ),  and  C(i$+o-i), 
Z>(2j+il-o). 

65.  To  Draw  the  Projections  of  a  Straight  Line  2"  long 
Making  an  Angle  45°  with  H  and  an  Angle  of  30°  with  V. 


108 


MECHANICAL  DRAWING 


ist.  Assume  the  point  a  in  H,  Fig.  112,  and  draw  through 
it  line  ab  2"  long,  making  an  angle  of  30°  with  G.L.  a'b'z 
is  its  V  projection. 

2d.  At  the  point  a'  draw  a'b'\  2"  long,  making  an  angle  of 
45°  with  G.L.  ab\  is  its  H  projection. 


b    5, 


3d.  Using  •#  and  a'  as  centers  and  ab\  and  a'bf2  as  radii 
describe  arcs  cutting  lines  parallel  to  G.L.  through  62  and  b\ '  in 
the  points  b  and  b'. 

4th.  Join  a  and  b  and  a'  and  br  with  straight  lines.  They 
are  the  projections  required. 

PROB.  43.  Draw  the  projections  of  a  line  making  an  angle 
of  30°  with  H  and  an  angle  of  45°  with  V. 


CHAPTER  VII 
ORTHOGRAPHIC  PROJECTION  APPLIED 

THE  problems  in  this  chapter  give  an  opportunity  for  the 
student  to  apply  the  principles  of  orthographic  projection 
to  the  making  of  practical  working  drawings. 

66.  PLATE  12.  This  plate  will  consist  of  eight  complete 
projections  of  solids  of  various  forms  and  familiar  outlines. 
Divide  the  plate  into  9  equal  spaces,  as  shown  in  Fig.  113. 

Fig.  114  shows  an  isometric  drawing  of  a  wedge  in  which 
there  are  eight  principal  points  which,  when  properly  projected 
according  to  the  principles  given  in  Art.  47  and  joined  in 
correct  order  with  straight  lines  will  produce  a  complete 
mechanical  drawing  in  three  views. 

PROB.  44.  In  the  upper  left-hand  space  on  the  plate  draw  the 
V,  H  and  P  projections  of  the  wedge  shown  in  Fig.  114. 

This  problem,  like  all  the  others  in  Plate  12,  is  to  be 
drawn  very  carefully  and  accurately  with  fine,  narrow  lines, 
using  the  6H  pencil  properly  sharpened.  Each  problem, 
when  completed  should  be  submitted  for  approval  and  when 
correct  in  every  particular  it  should  be  checked  by  the  in- 
structor and  directions  given  for  the  next  problem. 

PROB.  45.  The  same  wedge  used  in  Prob.  44  is  to  be  drawn  in 
space  2,  but  in  a  reversed  position,  as  shown  in  Fig.  113.  Draw 
the  V,  H  and  P  projections. 

It  will  bfe  noticed  in  the  plate  layout,  Fig.  113,  that  the  P 
projection  in  Probs.  44  and  45  is  revolved  by  two  different  meth- 
ods. The  first  by  arcs  of  circles,  centered  at  the  point  of  inter- 
section of  P  and  G.  L.  the  second  by  straight  lines  drawn 
from  the  points  to  be  revolved  to  the  bisector  of  the  angle.  The 
bisector  is  a  line  drawn  through  the  same  point  of  intersection 

109 


110 


MECHANICAL  DRAWING 


and  making  the  angle  of  45°  with  G.  L.  The  latter  method  is 
the  most  convenient  since  the  revolution  can  be  accomplished 
by  drawing  straight  lines  with  the  T-square  and  triangle. 

PLATE  12 


cu 

I 


v® 


J 


\ 


! 


n 

CJ 


isrt— 1 
" 


PROB.  47.    Given  the  V  and  P  projections  of  the  rectangular 
pyramid  illustrated  in  Fig.  115.    Find  and  draw  the  H  projection. 


ORTHOGRAPHIC  PROJECTION  APPLIED 


111 


For  the  definition  of  a  rectangular  pyramid,  see  Art.  31, 
No.  O  74. 

PROB.  48.  Given  the  H  projection  of  a  pentagonal  pyramid 
draw  the  V  and  P  projection.  Fig.  116. 


FIG.  114. 


FIG.  115. 


FIG.  116. 


Draw  the  pentagon  by  the  method  shown  in  Prob.  10,  Fig.  50, 
page  56. 

PROB.  49.  Given  the  plan  of  an  H- shaped  solid,  draw  the 
elevation  and  right-end  view.  Fig.  117, 


112 


MECHANICAL  DRAWING 


PROB.  50.     Given  the  front  elevation  and  end  elevation  of  a 
cross-shaped  solid,  draw  the  plan.     Fig.  118. 


FIG.  117. 


FIG.  1 1 8. 


PROB.  51.    Given  the  elevation    and  plan  of  the   rectangular 
box  shown  in  Fig.  119.     Draw  the  right-end  elevation. 


FIG.  i 19. 


FIG.  120. 


PROB.  52.  Given  the  V  projection  of  the  L-shaped  solid 
shown  in,  Fig.  120.  Draw  the  H  and  P  projections. 

When  all  the  problems  in  Plate  12  have  been  drawn 
correctly  in  fine  lines  and  checked,  the  plate  should  be  cleaned 


ORTHOGRAPHIC  PROJECTION  APPLIED  113 

with  art  gum  and  the  object  lines  of  all  the  drawings  strength- 
ened with  the  4H  pencil  properly  sharpened. 

2d.  The  dimension  lines  should  next  be  drawn,  very  nar- 
row with  the  6H  pencil. 

3d.  Put  on  all  dimension  figures  and  arrow  points,  first 
the  left-hand  arrow  point  then  the  dimension  and  sign  of 
inches  and  then  the  right-hand  arrow  point. 

Instead  of  the  problem  numbers  i,*2,  3,  etc.,  as  given  in 
Fig.  113,  use  the  numbers  of  problems  given  in  the  text  as  44, 
45,  etc.,  thus  "  Prob.  44."  Letters  &"  and  figures  A"  high. 

4th.  Letter  the  title  in  space  reserved  in  lower  right-hand 
corner  observing  the  directions  given  for  title  in  Plate  2, 
Art.  35.  The  main  title  to  be  "  Ortho.  Projection." 

5th.  Ink  border  line,  problem  numbers,  and  title. 

67.  PLATE  13.     Draw   the   rectangular   prism,   Fig  121,  in 
eight  different  positions  similar  to  the  position 
of  the   square   pyramid    shown    in    Fig.    122, 
and  according  to  the  directions  given  below. 

PROB.  53.  Given  the  elevation  and  plan  of 
the  prism,  Fig.  121  draw  the  end  view. 

Prob.  54.  Given  the  same  prism  of  problem 
53  when  the  plan  has  been  rotated  to  the  left 
through  an  angle  of  15°.  Project  the  front  and  end  elevations. 

PROB.  55.  Given  the  front  elevation  of  the  figure  obtained  in 
problem  54  when  revolved  to  the  left  through  an  angle  of  15°.  Draw 
the  plan  and  end  elevation. 

PROB.  56.  Given  the  front  elevation  of  problem  53  when  revolved 
through  an  angle  of  30°  to  the  right.  Draw  the  plan  and  end  view. 

PROB.  57.  Given  the  end  elevation  of  the  pyramid  obtained  in 
Prob.  54  when  revolved  to  the  right  through  an  angle  ofi$°.  Project 
the  front  elevation  and  plan. 

PROB.  58.  Given  the  end  view  of  the  pyramid  obtained  in 
Problem  55  when  revolved  to  the  left  through  an  angle  of  45°.  Draw 
the  front  elevation  and  plan. 

PROB.  59.  Given  the  end  view  of  the  pyramid  obtained  in 
Problem  56  when  revolved  through  an  angle  of  30°  to  the  left.  Draw 
the  elevation  and  plan. 


114 


MECHANICAL  DRAWING 


FIG.  122, 


FIG.  123. 


ORTHOGRAPHIC  PROJECTION  APPLIED 


115 


PROB.  60.  Given  the  front  elevation  obtained  in  Problem  57 
when  revolved  30°  to  the  right.  Draw  plan  and  end  view. 

67.  Auxiliary  Planes.  It  is  sometimes  necessary  to  show 
a  detail  of  a  machine  or  a  section  on  a  plane  oblique  to 
the  principal  planes  of  projection.  Such  planes  are  called 
auxiliary  planes. 

PLATE  14.  This  plate  will  consist  of  five  problems  to 
illustrate  the  use  of  the  auxiliary  plane. 

PROB.  61.  Given  the  elevation  and  plan  of  the  hollow  wedge- 
shaped  piece  shown  in  Fig.  123. 

i st.  Draw  an  end  view  of  the  wedge  at  the  left  of  the 
position  of  the   V  projection,   shown  in  Fig.   124,  taking  the 
dimensions  from  Fig.    123,   and  arrange  the  views  in  a  con- 
venient manner  in  the  upper  left-hand 
corner  of  the  plate. 

2d.  Draw  the  auxiliary  P  line  making 
30°  with  P  and  draw  an  auxiliary  ground 
line  at  right  angles  to  the  auxiliary  P 
line,  as  shown  in  Fig.  124. 

3d.  Draw  fine,  narrow  lines  from 
principal  points  in  elevation  perpen-  FlG  I24 

dicular  to  auxiliary  P  line. 

4th.  Draw  perpendicular  lines  from  corresponding  points 
in  the  plane  to  the  P  line  extending  them  to  intersect  the 
bisector  of  the  angle  between  P  and  the  auxiliary  G.L. 


FIG.  125.  FIG.  1250. 

5th.  From  the  points  of  intersection  on  the  bisector,  draw 
lines  perpendicular  to  the  auxiliary  G.L.  to  meet  the  corre- 
sponding lines  frcm  the  elevation  and  complete  the  auxiliary 
view  similar  to  the  partly  drawn  view  shown  in  Fig.  124. 


116 


MECHANICAL  DRAWING 


PROB.  62.    Arrange  the  front  and  end  view  of  the  hexagonal 
pyramid  given  in  Fig.  125/0  obtain  an  auxiliary  view  looking  in  a 


FIG.  126. 


V. 


FIG.  127. 


FIG.  128. 


direction  perpendicular  to  the  auxiliary  G.L.  which  is  to  make  an 
angle  of  30°  with  H,  as  shown  in  Fig.  1250. 


ORTHOGRAPHIC  PROJECTION  APPLIED 


117 


PROB.  63.  Given  the  elevation  and  plan  of  the  wedge  shown  in 
Fig.  126.  Draw  an  auxiliary  view  looking  in  the  direction  as  indi- 
cated in  Fig.  127. 

PROB.  64.  Given  the  plan  and  elevation  of  the  pipe  elbow  shown 
in  Fig.  128.  Draw  an  auxiliary  view  perpendicular  to  the  face  of 
the  inclined  flange.  This  view  will  give  the  true  size  of  the  flange 
and  the  holes  through  it. 


\ 


FIG.  129. 

PBOB.  65.  Given  the  elevation  and  plan  of  the  square  prism 
penetrated  by  the  hexagon  prism  as  shown  in  Fig.  129.  Draw  an 
auxiliary  view  perpendicular  to  the  hexagon  prism. 

In  laying  out  the  drawing  of  the  elevation  and  plane, 
draw  all  the  center  lines  first. 

2d.  Draw  the  inscribed  circle  of  the  square  prism  in  the 
plan  and  project  the  sides  to  the  front  view. 

3d.  On  the  center  line  of  the  hexagonal  prism  construct  a 
hexagon  whose  inscribed  circle  shall  be  equal  to  if". 


118  MECHANICAL  DRAWING 

4th.  From  the  six  corners  of  the  hexagon  draw  the  sides 
of  the  hexagonal  prism  in  the  elevation. 

5th.  Draw  the  auxiliary  view  as  required  and  determine 
the  V  and  H  projections  of  the  lines  of  intersection  between 
the  hexagonal  and  square  prism. 

Main  title.  "  Projection  on  Auxiliary  Plane."  This  plate 
is  to  be  finished  in  pencil.  Ink  title,  problem  numbers  and 
border  line. 


SECTIONS 

68.  Intersections  and  Developments. 

SECTIONS.  When  an  object  is  cut  by  a  plane  the  surface 
seen  when  a  part  is  removed  is  called  a  section. 

When  it  is  difficult  to  show  the  interior  construction  of 
an  object  by  invisible  lines,  it  is  usual  to  pass  a  cutting  plane 
through  that  part  of  the  object  desired  to  be  shown  and 
when  the  part  to  the  right  or  left  of  the  cutting  plane  is 
removed  there  is  obtained  what  is  called  a  sectional  view. 

INTERSECTION.  The  piercing  point  of  a  line  where  it 
penetrates  a  plane  is  the  point  of  intersection  between  the 
line  and  the  plane. 

The  line  in  which  two  planes  cut  each  other  is  called  the 
line  of  intersection. 

It  is  often  necessary  to  determine  the  true  form  of  the 
straight  or  curved  lines  of  intersection  in  representing  draw- 
ings correctly  or  in  developing  sheet  metal  work. 

DEVELOPMENTS.  If  the  surface  of  an  object  be  unwrapped 
upon  a  plane  until  every  part  of  that  surface  is  in  contact 
with  the  plane,  in  its  true  size,  the  surface  obtained  is  called 
a  development  of  the  surface  of  the  object. 

69.  Given  the  hexagon  prism  shown  in  Fig.  130,  cut  by  two 
planes.     Draw  the  development  of  the  lower  half  of  the  prism 
shown  in  the  elevation  as  follows: 

i st.  Draw  the  cutting  plane  at  an  angle  of  30°  so  that 
the  prism  is  divided  into  two  equal  parts. 


ORTHOGRAPHIC  PROJECTION  APPLIED 


119 


2d.  Draw  a  turned  section  on  an  auxiliary  plane  shown  at 
,i,  2,  3,  4. 

3d.  Lay  out  the  development  of  the  lower  half  of  the 
prism  thus: 

To  the  right  of  the  elevation  in  Fig.  130,  prolong  the  base 


FIG.  131. 


line  indefinitely  and  lay  off  upon  it  the  distances  ab,  be,  cd, 
etc.,  Fig.  131,  each  equal  in  length  to  a  side  of  the  hexagon. 
At  these  points  erect  perpendiculars,  and  through  the  points 
i  2  '3 V  draw  horizontal  lines  intersecting  the  perpendiculars 
in  4,  3,  2,  i,  etc.  At  be  draw  the  hexagon  aW,  chch,  dh 
of  the  last  problem  for  the  base,  and  at  i,  2  draw  the  sec- 
tion i,  2,  3,  4,  5,  6  for  the  top. 


120  MECHANICAL  DRAWING 

Fig.  131  shows  three  sides  of  the  lower  half  of  the  prism. 
The  remaining  three  may  be  drawn  in  a  similar  manner. 

PLATE  15.  This  plate  will  consist  of  sections  and  devel- 
opments. The  problems  are  to  be  worked  out  in  fine  pencil 
lines,  using  the  6H  pencil.  Each  problem  when  drawn  should 
be  submitted  for  criticism.  The  student  should  not  begin  a 
new  problem  until  the  preceding  has  been  approved  and 
checked  off.  When  the  drawings  of  all  the  problems  have 
been  approved,  the  plate  should  be  cleaned  with  the  art  gum 
and  all  lines  strengthened  with  the  4.H  pencil.  The  title  of 
this  plate  will  be  "  Sections  and  Developments."  Ink  only 
problem  numbers,  title  and  border  lines. 

PROB.  66.  Draw  the  elevation  and  plan  of  the  pentagonal 
prism  shown  in  Fig.  132. 

Pass  a  cutting  plane  B  dividing  the  elevation  of  the  prism 
into  two  equal  parts  at  an  angle  of  30°  and  develop  the  lower  half 
of  the  prism. 

i  st.  Project  the  true  form  and  size  of  the  section  cut  by 
Plane  B  upon  an  auxiliary  plane  and  draw  the  development 
of  the  lower  half  in  a  similar  manner  to  that  shown  in  Art.  69, 
Fig.  131,  for  a  hexagonal  prism. 

2d.  Add  the  plane  of  the  base  and  the  plane  of  the  section 
at  B  in  their  true  sizes  to  the  development. 

3d.  Draw  the  trace  of  Plane  A  in  the  position  shown  in 
the  plan,  Fig.  132,  conceive  the  part  to  the  right  removed  and 
draw  the  section  cut  by  Plane  A. 

PROB.  67.  Given  elevation  and  plan  of  pyramid  shown 
in  Fig.  133.  Pass  cutting  planes,  one  to  cut  the  elevation 
at  an  angle  of  45°  and  another  perpendicular  to  H  about 
in  the  positions  shown  by  the  traces. 

i  st.  Draw  the  center  lines  for  the  elevation  and  plan  of 
the  pyramid. 

2d.  Construct  the  outline  of  the  plan  to  dimensions  and 
join  the  four  corners  by  diagonal  lines. 

-3d.  From  the  point  of  intersection  between  the  diagonals 
draw  the  axis  of  the  pyramid  and  construct  the  elevation. 

4th.  Draw  the  trace  of  the  cutting  plane  through  the  ele- 


ORTHOGRAPHIC  PROJECTION  APPLIED 


121 


vation  at  an  angle  of  45°  and  draw  the  H  projection  of 
the  section. 

5th.  Draw  the  true  size  of  the  section  projected  in  lines 
perpendicular  to  the  trace  of  the  plane. 

6th.  Draw  the  full  development  of  the  lower  half  of  the 
pyramid  including  the  base  and  top. 

7th.  Prolong  the  cutting  plane  through  the  H  projection 
to  cut  the  V  projection  and  draw  the  true  size  of  the  section 
to  the  right  of  the  H  projection  of  the  pyramid. 


FIG.  132. 


FIG.  133. 


70.  Fig.  134.  To  draw  the  projections  of  a  right  cylinder 
3"  diameter  and  3"  long,  (i)  When  its  axis  is  perpendicular 
to  the  H.P.  (2)  Draw  the  true  form  of  a  section  of  the  cylin- 
der, when  cut  by  a  plane  perpendicular  to  the  V.P.  maLing 
an  angle  of  30°  with  the  H.P.  (3)  Draw  a  development  of 
the  upper  part  of  the  cylinder. 

For  the  plan  of  the  first  condition,  describe  the  circle  i', 
2',  etc.,  with  a  radius  =  if "  and  from  it  project  the  elevation, 
which  will  be  a  square  of  3"  sides. 

For  the  second  condition:  Let  i,  7  be  the  trace  of  the 
cutting  plane,  making  the  point  7,  f"  from  the  top  of  the 
cylinder.  Divide  the  circle  into  12  equal  parts  and  let  fall 
perpendiculars  through  these  divisions  to  the  line  of  section, 
cutting  it  in  the  points  i,  2,  3,  4,  etc.  Parallel  to  the  line 
of  section  i,  7  draw  i"  7"  at  a  convenient  distance  from  it, 
and  through  the  points  i,  2,  3,  4,  etc.,  draw  perpendiculars 
to  i,  7,  intersecting  and  extending  beyond  i"  7".  Lay  off 
on  these  perpendiculars  the  distances  6"  8"  =  6'  8',  and 


122 


MECHANICAL  DRAWING 


5"  9"  =  5'  9',  etc.,  and  through  the  points  2",  3",  4",  etc., 
describe  the  ellipse. 

For  the  development:  In  line  with  the  top  of  the  eleva- 
tion draw  the  line  g'g"  equal  in  length  to  the  circumference  of 
the  circle,  and  divide  it  into  12  equal  parts  a' ',  b',  etc.,  a',  b", 
etc.  Through  these  points  drop  perpendiculars  and  through 
the  points  i,  2,  3,  etc.,  draw  horizontals  intersecting  the 
perpendiculars  in  the  points  i,  2,  3,  etc.,  and  through  these 
points  draw  a  curve. 


.  Iff 


FIG.  134. 

Tangent  to  any  point  on  the  straight  line  draw  a  3"  circle 
for  the  top  of  the  cylinder  and  tangent  to  any  suitable  point 
on  the  curve  transfer  a  tracing  of  the  ellipse. 

PROB.  68.  Draw  the  projections  of  a  right  cylinder  4" 
diameter  and  4!"  long.  Cut  by  a  plane  making  an  angle  of 
30°  with  H  and  dividing  the  cylinder  into  two  equal  parts. 

Draw  the  true  size  of  the  section  cut  by  the  plane  and 
develop  the  lower  half  of  the  cylinder  in  a  similar  manner 
to  that  shown  in  Fig.  134. 

71.  FIG.  135.  To  draw  the  development  of  the  half  of 
a  truncated  cone,  given  the  plan  and  elevation  of  the  cone. 


ORTHOGRAPHIC  PROJECTION  APPLIED 


123 


Divide  the  semicircle  of  the  plan  into  any  number  of  parts, 
then  with  A  as  center  and  Ai  as  radius,  draw  an  arc  and  lay 
off  upon  it  from  the  point  i  the  divisions  of  the  semicircle 
from  i  to  9,  draw  gA.  Then  with  center  A  and  radius  AB 
draw  the  arc  BC.  iBCg  is  the  development  of  the  half  of 
the  cone  approximately. 

PROB,  69.    Given  a.  right  'circular  cone  whose   base  is  3" 


diameter  and  height  4"  intersected  by  a  V  projecting  plane. 
The  trace  of  the  plane  to  pass  through  the  center  of  the  axis 
and  make  30°  with  H. 

Find  the  true  size  of  the  section  and  lay  out  the  full 
development  of  the  lower  part  of  the  cone.  Scale:  6"  =  i'. 

72.  FIG.  136.  To  draw  the  projections  of  a  right  cone 
7"  high,  with  a  base  6"  in  diameter,  pierced  by  a  right  cyl- 
inder 2"  in  diameter  and  5"  long  their  axes  intersecting  at 


124  MECHANICAL  DRAWING 

right  angles  3"  above  the  base  of  the  cone  and  parallel  to 
V.P.     Draw  first  the  plan  of  the  cone  with  a  radius  =  3". 

At  a  convenient  distance  below  the  plan  draw  the  eleva- 
tion to  the  dimensions  required. 

Three  inches  above  the  base  of  the  cone  draw  the  center 
line  of  the  cylinder  CD,  and  about  it  construct  the  elevation 
of  the  cylinder,  which  will  appear  as  a  rectangle  2"  wide  and 
2§"  each  side  of  the  axis  of  the  cone.  The  half  only  appears 
in  the  figure. 

To  project  the  curves  of  intersection  between  the  cylinder 
and  cone  in  the  plan  and  elevation:  Draw  to  the  right  of 
the  cylinder  on  the  same  center  line  a  semicircle  with  a  radius 
equal  that  of  the  cylinder.  Divide  the  semicircle  into  any 
number  of  parts,  as  i,  2,  3,  4,  etc.  Through  i,  i  draw  the 
perpendicular  A"  i"  equal  in  length  to  the  height  of  the  cone, 
and  through  A"  draw  the  line  A"  4"  tangent  to  the  semi- 
circle at  the  point  4,  and  through  the  other  divisions  of  the 
semicircle  draw  lines  from  A"  to  the  line  i"  4" ',  meeting  it 
in  the  points  3"  2" . 

From  all  points  on  the  line  i"  4",  viz.,  i",  2" ',  3",  4", 
erect  perpendiculars  to  the  center  line  of  the  plan,  cutting 
it  in  the  points  ii",  21",  31",  41",  and  with  i/'  as  the  center 
draw  the  arcs  2i"-2,  31^-3,  4i"-4  above  the  center  line  of 
the  plan,  and  through  the  points  2,  3,  4,  draw  horizontals 
to  intersect  the  circle  of  the  plan  in  the  points  2',  3',  4', 
and  lay  off  the  same  distances  on  the  other  sides  of  the  center 
line  of  the  plan  in  same  order,  viz.,  2',  3',  4'.  Through  each 
of  these  points  on  the  circumference  of  the  circle  of  the  plan 
draw  radii  to  its  center  A' ',  and  through  the  same  points  also 
in  the  plan  let  fall  perpendiculars  to  the  base  of  the  elevation 
of  the  cone,  cutting  it  in  the  points  2',  3',  4';  and  from  the 
apex  A  of  the  elevation  of  the  cone  draw  lines  to  the  points 
2',  3',  4'  on  the  base.  Horizontal  lines  drawn  through  the 
points  of  division  2,  3,  4,  on  the  semicircle  will  intersect  the 
elements  A-2* ',  ^-3',  A-A?  of  the  cone  in  the  points  2',  3',  4'; 
these  will  be  points  in  the  elevation  of  the  curve  of  inter- 
section between  the  cylinder  and  the  cone. 


ORTHOGRAPHIC  PROJECTION  APPLIED 


125 


The  plan  of  the  curve  is  found  by  erecting  perpendiculars 
through  the  points  in  the  elevation  of  the  curve  to  intersect 
the  radial  lines  of  the  plan  in  correspondingly  figured  points, 
through  which  trace  the  curve,  as  shown.  Repeat  for  the 
other  half  of  the  curve. 

FIG.  137.  To  draw  the  development  of  the  half  cone, 
showing  the  hole  penetrated  by  the  cylinder. 


FIG.  136. 


FIG.  137. 


With  center  4/',  and  element  Aif  of  the  cone.  Fig.  136, 
as  radius,  describe  an  arc  equal  in  length  to  the  semicircle 
of  the  base  of  the  cone.  Bisect  it  in  the  line  4/',  i,  and  on 
each  side  of  the  point  i  lay  off  the  distances  2,  3,  4,  equal 
to  the  divisions  of  the  arc  in  the  plan  Fig.  136,  and  from  these 
points  draw  lines  to  4",  the  center  of  the  arc.  Then  with 
radii  A-a,  b,  i,  d,  e,  respectively,  on  the  elevation  Fig.  136, 


126 


MECHANICAL  DRAWING 


and  center  4/'  draw  arcs  intersecting  the  lines  drawn  from 
the  arc  XX  to  its  center  4/'.  Through  the  points  of  inter- 
section draw  the  curve  as  shown  by  Fig.  137. 

PLATE  16.  This  plate  will  consist  of  lines  of  intersection 
and  developments.  Arrange  drawings  on  plate  to  best  advantage. 

PROB.  70.  Draw  the  projections  of  a  right  circular  cone 
with  a  3"  base  and  4"  high,  pierced  by  a  right  cylinder  i%" 
diameter.  The  center  line  of  the  cylinder  to  be  i|"  above  the 
base  of  the  cone. 

i  st.  Find  the  curve  of  intersection  between  the  cylinder 
and  the  cone  according  to  Art.  72. 


FIG.  138. 


FIG.  139. 


id.  Draw  the  development  of  half  of  the  cone  showing  the 
hole  made  by  the  penetration  of  the  cylinder.  Scale:  i2"  =  i'. 

73.  To  find  the  curve  of  intersection  between  two  right 
cylinders  intersecting  each  other  at  right  angles. 

Fig.  138  shows  three  views  of  two  right  cylinders  of  equal 
diameter,  intersecting  at  right  angles. 

i  st.  Divide  the  semi-circle  in  the  plan  into  12  equal  parts 
and  from  the  points  on  one-quarter  of  the  circumference  draw 
horizontals  to  meet  the  bisector  of  the  90°  angle  of  revolu- 
tion and  from  those  points  drop  perpendiculars  to  cut  cir- 
cumference of  the  circle  in  the  end  view  of  the  other  cylinder. 

2d.  From  the  same  points  in  the  plan  drop  perpendicu- 
lars to  meet  horizontals  drawn  from  the  corresponding  points 
in  the  end  view. 


ORTHOGRAPHIC  PROJECTION  APPLIED 


127 


3d.  Draw  the  curve  of  intersection  through  the  points 
of  intersection  between  the  perpendiculars  and  horizontals  in 
the  front  view.  The  curve  in  this  case  will  be  a  straight  line 
because  the  intersecting  cylinders  are  equal  in  diameter. 

PROB.  71.  Draw  the  curve  of  intersection  between  the  two 
right  cylinders  shown  in  Fig.  139,  to  the  dimensions  given,  and 
development  of  small  cylinder. 

This  line  of  intersection  will  be  an  irregular  curve.  When 
the  points  in  the  curve  are  obtained,  sketch  freehand  a  light 
line  through  them, 
making  a  smooth 
curve,  and  when 
finishing  the  draw- 
ing strengthen  the 
line  with  the  4H 
pencil  and  the 
French  curve. 

Study  Arts.  70 
and  73. 

PROB.  72.  Given 
the  elevation  and 
plan  of  the  square 
prism  penetrated  by 
a  hexagonal  prism, 
Fig.  139^.  Draw 
the  development  of 
either  the  square 
prism  or  the  hexag- 
onal prism  showing 
the  true  size  of  the 
part  remaining  of 
one  after  the  other 
has  been  removed.  Scale:  to  suit. 

See  Appendix  to  Mechanical  Drawing  for  additional  prob- 
lems in  intersections  and  developments.  - 


CHAPTER  VIII 

ISOMETRICAL    PROJECTION 

74.  In  orthographic  projection  it  is  necessary  to  a  correct 
understanding  of  an  object  to  have  at  least  two  views,  a 
front  and  end  elvation  or  an  elevation  and  plan,  and  some- 
times even  three  views  are  required. 

Isometric  projection  on  the  other  hand  shows  an  object 
completely  with  only  one  view.  It  is  a  very  convenient 
system  for  the  workshop.  Davidson  in  his  Projection  calls 
it  the  "  Perspective  of  the  Workshop."  It  is  more  useful 
than  perspective  for  a  working  drawing,  because,  as  its  name 
implies  ("  equal  measures  ")  it  can  be  made  to  any  scale  and 
measured  like  an  orthographic  drawing.  It  is,  however, 
mainly  employed  to  represent  small  objects,  or  large  objects 
drawn  to  a  small  scale,  whose  main  lines  are  at  right  angles 
to  each  other. 

The  principles  of  isometrical  projection  are  founded  on  a 
cube  resting  on  its  lower  front  corner,  i,  Fig.  140,  and  its  base 
elevated  so  that  its  diagonal  AB  is  parallel  to  the  horizontal 
plane.  Then,  if  the  cube  is  rotated  on  the  corner  i  until 
the  diagonal  AB  is  at  right  angles  to  the  vertical  plane,  i.e., 
through  an  angle  of  90°,  the  front  elevation  will  appear  as 
shown  at  i,  2,  3,  4,  Fig.  140,  a  regular  hexagon. 

Now  we  know  that  in  a  regular  hexagon,  as  shown  by 
Fig.  140,  the  lines  lA,  A 3,  etc.,  are  all  equal,  and  are  easily 
drawn  with  the  3o°X6o°  triangle.  But,  although  these  lines 
and  faces  appear  to  be  equal,  yet,  being  inclined  to  the  plane 
of  projection,  they  are  shorter  than  they  would  actually  be 
on  the  cube  itself.  However,  since  they  all  bear  the  same 

128 


ISOMETRICAL  PROJECTION 


129 


proportion  to  the  original  sizes,  they  can  all  be  measured 
with  the  same  scale. 

75.  To  make  an  isometrical  scale. 

Draw  the  half  of  a  square  with  sides  =  i\",  Fig.  141. 
These  two  sides  will  make  the  angle  of  45°  with  the  horizontal 


FIG.  140. 

Now  the  sides  of  the  corresponding  isometrical  squares,  we 
have  seen,  makes  the  angle  of  30°  with  the  horizontal,  so  we 
will  draw  i,  4,  3,  4,  making  angles  of  30°  with  i,  3.  The 


FIG.  141. 


difference  then  between  the  angle  2,  i,  3  and  the  angle  4,  i,  3 
is  15°,  and  the  proportion  of  the  isometrical  projection  to  the 
actual  object  is  as  the  length  of  the  line  3,  2  to  the  line  3,  4. 
And  if  the  line  3,  2  be  divided  into  any  number  of  equal 
parts,  and  lines  be  drawn  through  these  divisions  parallel  to 


130 


MECHANICAL  DRAWING 


2,  4  to  cut  the  line  3,  4  in  corresponding  divisions,  these 
will  divide  3,  4  proportionately  to  3,  2. 

Now  if  the  divisions  on  3,  2  be  taken  to  represent  feet 
and  those  on  3,  4  to  represent  2  feet,  then  3,  4  would  be  an 
isometrical  scale  of  ^. 

76.  Isometrical  Drawing.  Since  isometrical  drawings  may 
be  made  to  any  scale,  we  may  make  the  isometrical  lines  of 


FIG.  142. 

the  object  =  their  true  size.    This  is  a  common  practice  and 
precludes  the  need  of  a  special  isometrical  scale. 

When  an  object  is  drawn   to  its   true   size  the   result  is 
called  an   Isometrical  Drawing. 


ISOMETRICAL  PROJECTION 


131 


Fig.  142  gives  a  detail  isometric  drawing  of  the  f"  globe 
valve  shown  in  the  piping  layout. 

Fig.  143  shows  an  isometric  drawing  of  an  engine  connect- 
ing rod  partly  in  section. 


FIG.  143. 


Fig.  144  shows  an  isometrical  drawing  made  by  the  Mur- 
ray Engine  Works.  It  represents  in  one  view  the  layout  of  a 
power  plant. 

Fig.  145  shows  a  detail  isometric  drawing  of  the  layout 
of  the  steam  piping  for  the  above  power  plant. 

Fig.  146  shows  an  isometric  drawing  of  an  engine  con- 
necting rod. 


132 


MECHANICAL  DRAWING 


ISOMETR1CAL  PROJECTION 


133 


134 


MECHANICAL  DRAWING 


ISOMETRICAL  PROJECTION 


135 


77.  To  make  the  isometrical  drawing  of  a  two-armed 
cross  standing  on  a  square  pedestal. 

Begin  by  drawing  a  center  line  AB,  Fig.  147,  and  from  the 
point  A  draw  AC  and  AD,  making  an  angle  of  30°  with  the 


horizontal.  Measure  from  A  on  the  center  line  AB  a  dis- 
tance =  T&"y  and  draw  lines  parallel  to  AC,  AD]  make  AC 
and  AD  2%"  long  and  erect  a  perpendicular  at  D  and  C} 
completing  the  two  front  sides  of  the  base,  etc. 

Note:  Measurements  should  always  be  made  along  an 
isometric  line. 

78.  To  Draw  the  Isometric  Projection  of  a  Circle  on  a 
Horizontal  Plane. 

Draw  a  2"  circle  and  describe  an  orthographic  square 
about  it,  using  the  45°  triangle,  Fig.  148. 

Draw  the  diagonals  i,  2,  3,  4  and  the  diameters  5,  6,  7,  8 
at  right  angles  to  each  other. 

Now  from  the  points  i  and  2  draw  lines  iA,  iB  and  2.4, 
2B,  making  angles  of  30°  with  the  horizontal  diagonal  i,  2. 


136 


MECHANICAL  DRAWING 


And  through  the  center  0  draw  CD  and  EF  Sit  right  angles 
to  the  isometrical  square. 

The  points  CD,  EF,  and  GH  will  be  points  in  the  curve 

of  the  projected  isometrical  circle,  which  will  be  an  ellipse. 

The  ellipse  may  be  drawn  sufficiently  accurate  as  follows: 

With  center  B  and  radius  BC  describe   the   arc  CF  and 

extend  it  a  little  beyond  the  points  C  and  F,  and  with  center 

A  and  same  radius  describe  a  similar  arc,  then  with  a  radius 

which   may   readily   be    found   by    trial,    draw    arcs    through 

G  and   H.     These  smaller  arcs  are  not  to  be  drawn  tangent 

to  the  sides  of  the  square  at  the  points  G,  D}  E,  or  F,  but 


are  to  be  drawn  tangent  to  the  larger  arcs  extended  beyond 
the  points  C,  D,  E,  and  F,  as  stated. 

This  gives  a  close  approximation  to  a  true  ellipse  and 
maintains  the  true  length  of  the  major  axis,  which  is  very 
desirable,  because  the  major  axis  must  always  remain  the 
same  length  whatever  the  angle  of  the  plane  may  be  in  which 
the  circle  is  projected. 

An  isometric  circle  drawn  in  this  way  presents  a  neat  and 
satisfying  appearance. 

79.  To  Find  the  Small  Radius  V  of  the  isometric  circle. 
With  OC,  Fig.  148,  as  radius  and  point  i  as  center,  cut  the 
major  axis  of  the  ellipse  in  i'.  i'  is  the  center  of  radius  v 
of  the  approximate  ellipse  or  isometric  circle. 


ISOMETRICAL  PROJECTION 


137 


The  use  of  this  method  for  determining  the  radius  pre- 
cludes the  need  of  drawing  the  orthographic  circle  or  square 
when  making  an  isometric  "  drawing  "  of  a  circle. 

80.  To  Make  the  Isometric  Drawing  of  a  Hexagonal 
Bolt  Head  on  a  Vertical  Plane.  Fig.  149. 

i st.  Draw  the  center  line  C  of  the  bolt  from  left  to  right, 
making  the  angle  of  30°  with  the  horizontal  and  another  line 


FIG.  149. 


D  at  30°  from  right  to  left,  cutting  the  first  line  at  the  center 
of  the  hexagon  and  through  the  same  center  draw  a  per- 
pendicular, as  shown  in  Fig.  149. 

2d.  Draw  the  isometric  square  with  sides  equal  to 
F=i%d+%"=the  distance  across  the  flats  of  the  hexagonal 
head. 

3d.  Draw  the  isometric  inscribed  circle  in  the  usual  way 
and  describe  the  hexagon  about  it  as  shown  in  the  figure, 
laying  off  the  long  diameter  of  the  hexagon  on  the  center  line 
D,  making  D=FX  1.155. 


138 


MECHANICAL  DRAWING 


4th.  Make  radius  R  equal  to  the  width  of  the  face  and 
all  the  edges  of  the  hexagonal  head  equal   to  each  other  in 


FIG.  150. 


length.     The  chamfer  curves  on  the  other  faces  may  be  easily 
drawn  by  trial  radii. 

Fig.  150  shows  the  isometric  "  projection "  of  the  same 
bolt  and  bolthead. 

81.  To  Lay  Off  an  Angle  on  an  Isometric  Circle. 

i  st.  Construct  the  ellipse  from  the  orthographic  circle  as 
explained  in  Art.  78. 

2d.  Lay  off  the  true  angle  A  as  shown  in  Fig.  151,  by  a 
dotted  line  and  when  this  line  cuts  the  orthographic  circle 
erect  a  perpendicular  to  the  ellipse  or  isometric  circle  and 
through  that  point  draw  a  line  from  the  center  making,  the 
corresponding  isometric  angle  a. 

This  method  can  be  used  in  determining  the  points  of  the 
hexagon  as  shown  at  Fig.  152  as  follows: 

Given  the  orthographic  and  isometric  circles,  draw  the 
broken  line'  through  the  center  of  the  circle,  making  an  angle 
of  60°  with  the  horizontal  (since  there  are  six  angles  of  60° 


ISOMETRICAL  PROJECTION 


130 


each  in  a  hexagon),  Fig.  152,  and  produce  it  to  cut  the  ortho- 
graphic circle,  as  shown  in  a  point.     Revolve  that  point  back 


FIG.  152. 


into  the  isometric  circle  by  drawing  a  line  through  the  point 
parallel  to  the  axis  to  intersect  the  isometric  circle  in  a 
corresponding  point.  From  the  center  draw  a  solid  line 
through  the  latter  point  and  produce  it  to  intersect  a  hori- 
zontal tangent  to  the  isometric  circle.  The  point  of  inter- 
section is  a  point  of  one  of  the  angles  of  the  isometric  hexa- 
gon. The  other  angles  may  be  found  in  a  similar  manner. 

82.  To  lay  off  an  angle  from  a  corner  of  the  isometrical 
cube. 

Construct  an  orthographic  square  of  any  convenient  size 
as  shown  in  Fig.  153  and  draw  the  required  angle  AOB. 


A  O 

FIG.  153. 


From  the  corner  of  the  isometrical  cube  where  the  angle  is 
to  be  drawn  lay  off  along  the  side  a  distance  equal  to  OA  of 


140 


MECHANICAL  DRAWING 


the  orthographic  square  and  erect  a  perpendicular  at  A. 
Step  off  the  distance  AB  and  draw  OB  the  angle  required. 
Any  other  angle  may  be  drawn  in  similar  manner. 


PLATE   i 7 

PROB.  73.  Make  the  isometrical  drawing  of  a  i\"  cube.  Draw 
a  2\"  isometric  circle  on  the  upper  face  by  the  method  shown  in 
Fig.  148,  page  136.  From  the  lower  left-hand  corner  of  the  right- 
hand  face  lay  off  angles  of  15°,  30°,  and  45°.  Use  method  shown 
in  Fig.  153. 

PROB.  74.  Make  the  isometrical  drawing  of  the  hollow  cube 
with  a  hollow  block  on  each  face  as  shown  in  Fig.  154. 


FIG.  154- 


PROB.  75.  Make  the  isometrical  drawing  of  a  hexagonal 
headed  bolt  and  nut  on  a  horizontal  plane  as  shown  in  Fig.  155. 

Follow  directions  given  in  Art.  80  and  make  drawing  similar 
to  Fig.  149.  Bolt  to  be  i 


ISOMETRICAL  PROJECTION 


141 


PROB.  76,    Fig.  156.    Make   the   isometrical   drawing   of    a 
pentagonal  prism.    Sides  i  J".     Height  of  prism  i\" . 

ist.  Construct  pentagon  of  ij"  sides  by  Prob.  50,  page  56. 
2d.  Through  the  point  A  on  the  vertical  axis  of  the  pentagon 


FIG.  155. 

draw  the  isometric  line  I'-s'  at  the  angle  of- 30°  to  the  left  and 
A,  3',  to  the  right. 

3d.  With  center  A  and  A,  i  as  radius  cut  points  i'  and  5'. 

4th.  Draw  through  o  the  isometric  line  o\o'  and  through  c 
the  line  2',  4'. 

5th.  Through  the  point  3  draw  3,  3'  to  intersect  A,  3'  in  the 


142 


MECHANICAL  DRAWING 


FIG.  157. 


ISOMETRICAL  PROJECTION 


143 


point  3'.  Join  the  points  i',  2',  3',  4'  and  5',  with  straight  lines 
completing  the  isometric  drawing  of  the  pentagon,  i',  5'  is 
the  only  isometric  line  in  the  pentagon  and  measures  the  exact 
size  of  the  side,  viz.,  i^". 

6th.  Finish  the  construction  of  the  prism  by  drawing  the 
edges  of  the  prism  downward  2  J"  long  and  connect  with  straight 
lines. 

PROB.  77.  Make  the  isometrical  drawing  of  the  tool  box,  shown 
at  Fig.  157,  to  the  dimensions  given. 

i  st.  Draw  the  box  in  isometric  as  shown. 

2d.  To  draw  the  isometric  of  the  cover  when  open  at  the  angle 
of  30°,  draw  the  end  view  of  the  box  orthographically  as  shown 
setting  the  cover  at  the  actual  angle  of  30°.  Fig.  158. 

3d.  Draw  the  broken  lines  i,  2;  3,  6  and  4,  5  horizontally 
through  the  corners  of  the  cover,  as  shown. 

4th.  At  the  point  a,  Fig.  158,  erect  the  perpendicular  broken 
line  a,  4  and  take  the  distance  a,  2,  Fig.  158,  and  lay  off  a',  2', 


FIG.  158. 


Fig.  157.  Draw  i',  2',  Fig.  157,  at  the  angle  of  30°.  With  the 
distance  1,2,  Fig.  158,  lay  off  i',  2',  Fig.  157. 

5th.  Take  the  distance  a,  3,  Fig.  158,  and  lay  off  a',  3',  Fig. 
157,  and  make  3',  6',  equal  to  3,  6. 

6th.  Make  a',  4'  equal  to  a,  4  and  4',  5'  equal  to  4,  5  and 
join  the  points  a',  i',  5',  and  6'  with  straight  lines. 


144 


MECHANICAL  DRAWING 


7th.  Complete  the  isometric  drawing  of  the  cover  and  place 
dimensions  as  shown. 

PROB.  78.  Find  the  line  of  intersection  on  the  2"  by  \\"  T 
coupling.  Fig.  159. 

i  st.  Draw  the  coupling  as  shown. 

2d.  On  the  center  line  of  o,  o  of  the  small  cylinder  describe  a 
semicircle  and  divide  it  in  to' 12  equal  parts,  from  o  to  6  and  from 
6  to  o. 

3d.  On  the  right-hand  end  of  the  large  cylinder,  at  the  center 
C  erect  a  perpendicular  C,  0' .  Of  is  the  top  of  the  cylinder. 


FIG.  159. 

4th.  At  point  0'  draw  a  perpendicular  to  the  isometric 
square  and  describe  the  same  semicircle  as  on  the  small  cylinder 
and  divide  it  from  o  to  6  as  before.  Through  these  points 
draw  lines  parallel  to  the  perpendicular  c^o',  cutting  the  large 
ellipse  in  points  o/  1/2',  etc. 

5th.  Through  points  o/  i1  '2',  etc.,  draw  lines  parallel  to 
the  axis  of  the  large  cylinder  to  intersect  the  corresponding  per- 
pendicular lines  from  the  same  points  on  the  small  cylinder. 

6th.  Through  the  resulting  points  draw  the  required  curve 
of  intersection. 


CHAPTER  IX 
WORKING  DRAWINGS 

83.  A  working  drawing  is  made  to  convey  all  the  neces- 
sary information  from  the  drafting  room  to  the  shop  to  enable 
the   workmen   to   correctly  make  a   pattern  for   castings,   to 
make  parts  to  be  forged  in  wrought  iron  or  soft  steel,  to  make 
parts   to   be  made   in   sheet   metal.     To   give    the   necessary 
information  to  the  machine  shop,  to  do  the  finishing  and  to 
the  fitting  shop  to  properly  assemble  the  different  parts  into 
the  whole  machine. 

84.  The   making   of  a  working   drawing  may   be    divided 
into   consecutive  steps  as  follows: 

i  st.  The  selection  of  the  proper  size  of  detail  paper  for  the 
drawing  or  drawings  to  be  made. 

In  most  drafting  rooms  standard  sizes  are  used  for  the 
different  details  to  be  drawn;  such  as  9"Xi2",  i2"Xi8", 
i8"X24",  etc. 

For  the  purposes  of  this  course  all  our  drawing  are  made  on 
sheets  i5"X2o"  over  all. 

2d.  Drawing  the  standard  border  line. 

The  border  line  will  be  the  same  for  all  drawings  ij"  at  left- 
hand  end  and  |"  at  top  and  bottom  and  right-hand  end. 

The  width  of  the  border  line  should  be  A". 

3d.  The  arrangement  of  the  different  details  to  be  placed  on  the 
sheet  including  the  necessary  mews  of  each  part. 

For  each  plate  a  definite  number  of  problems  will  be  assigned. 

The  draftsman  should  make  some  calculations  to  determine 
approximately  the  space  required  for  essential  views  of  the  dif- 
ferent objects  together  with  suitable  spaces  between  views  and 
between  the  different  problems,  having  in  mind  the  space  required 

itle  and  bill  of  material. 

145 


146  MECHANICAL  DRAWING 

Different  views  of  an  object  should  be  spaced  closer  together 
than  the  space  allowed  between  different  objects. 

4.  The  style,  location,  drawing  and  application  of  title,  bill  of 
material,  notes  and  dimension  figures. 

i.  The  style  of  the  title  is  given  in  Fig.  160.  The  guide  lines 
should  be  carefully  drawn  in  fine  light  lines  with  the  6n  pencil 
according  to  the  spacing  given. 

2d.  The  bottom  line  of  the  title  should  be  about  jV  inside 
of  the  border  line  in  the  lower  right-hand  corner  of  the  plate. 

3d.  The  longest  line  of  the  title  should  be  lettered  first  and 
a  light  vertical  line  drawn  through  the  center  of  it  so  that  the 
remainder  of  the  title  may  be  balanced  with  reference  to  that 
center  line. 

\J \ 


*w    » ;      ^jeEOMerm/GtfL. 


T     %k 


FIG.  i 60. 

4.  The  name  line  of  the  standard  title  should  be  inked  with 
heavy  lines  to  give  prominence. 

Ink  first  in  ordinary  lines  with  ball-point  pen  No.  516  and  then 
strengthen  the  lines  of  all  the  letters  of  the  words  in  the  main 
title,  using  the  Gillott  fine  pen  No.  303. 

In  drawing  the  bill  of  material  table,  observe  the  dimensions 
given  in  Fig.  161. 

Make  the  name  space  to  suit  the  longest  name  to  be  recorded, 
using  appropriate  abbreviation,  consulting  Section  30. 

The  bottom  line  of  the  bill  of  material  should  be  placed  J" 
above  the  top  line  of  the  title.  ;  , 

In  the  column  for  "  Number  "  of  pieces  any  number  may 
generally  be  recorded. 


WORKING  DRAWINGS 


147 


In  the  column  for  "  Remarks  "  state  any  suitable  information 
for  the  shop  not  given  on  the  drawing  such  a  patt.,  style,  etc. 

5.  Procedure  in  Making  Pencil  Drawing. 

i  st.  When  the  border  lines,  space  for  title  and  bill  of  material 
have  been  laid  off,  then  on  the  remaining  space  on  the  plate  lay 
out  the  center  lines  of  the  different  views  of  the  drawings  to  be 
made. 

2d.  Begin  at  the  upper  left-hand  corner  of  the  plate  and  draw 
the  different  views  of  the  first  object  to  be  drawn  in  fine  pencil 
lines.  Make  the  details  complete  and  when  all  the  views  have 
been  carefully  drawn  in  fine  narrow  lines  with  the  6n  pencil 
properly  sharpened  the  drawing  should  be  submitted  for 
approval.  If  it  is  all  right  or  when  it  is  made  right  the  instructor 
will  check  it  off  and  the  next  problem  may  be  drawn  in  a  similar 


vj_ 


^o—  'MR*. 


^/LL. 


MstfTEfUJL 


NO.  MIL. 


MS./. 


FIG.  161. 

manner  and  so  on  for  all  the  drawings  to  be  placed  on  the 
plate. 

3d.  When  the  drawings  have  all  been  checked  off  the  plate 
should  be  cleaned  with  art  gum  and  all  the  object  lines  strength- 
ened with  the  4H  pencil  properly  sharpened  to  give  a  strong, 
clear  line. 

4th.  The  dimension  lines  are  next  to  be  applied,  very  narrow, 
with  the  611  pencil,  and  also  guide  lines  for  information  notes. 

5th.  Put  on  all  dimensions  with  the  4H  pencil,  beginning  with 
the  left-hand  arrow  point,  then  the  dimension  and  sign  of  inches 
and  then  the  right-hand  arrow  point.  This  procedure  in 
placing  dimensions  should  be  observed  at  all  times  so  as  to 
avoid  leaving  off  arrow  points,  sign  of  inches,  figures,  etc. 

6th.   Letter  all  notes,  title,  bill  of  material  and  last  of  all 


148  MECHANICAL  DRAWING 

draw  the  crosshatching  lines  on  section  surfaces.  The  distance 
between  cross-hatch  lines  should  be  TG". 

7th.  The  student  should  next  check  his  drawing  for  errors 
that  it  may  be  as  correct  as  possible  before  submitting  for  final 
approval. 

6.  Tracing  and  Blue  Printing. 

1.  Drawings  these  days  are  often  made  directly  on  the  dull 
side  of  the  tracing  cloth  or  on  tracing  paper  and  then  inked. 
There  is  not  much  time  saved  in  this  method  except  when  prints 
are  to  be  gotten  out  in  a  hurry  without  much  regard  for  their 
appearance,  then  the  prints  are  made  directly  from  the  pencil 
drawing   without  inking.     In   this   way  prints   can   be   made 
quickly,  but  unless  the  exposure  is  accurately  made  the  result  is 
a  poor  print  with  a  liability  to  errors. 

2.  In  making  a  blue  print  from  a  tracing,  the  back  of  the 
tracing  is  placed  against  the  sensitized  surface  of  the  prepared 
print  paper  and  exposed  in  a  printing  machine  with  the  face  of 
the  tracing  toward  the  light. 

3.  The  time  of  exposure  must  be  learned  by  trial,  because 
there  is  often  much  difference  in  the  sensitiveness  of  the  print 
paper  and  also  in  the  transparency  or  opaqueness  of  the  tracing 
medium. 

4.  When  the  exposure  to  the  light  is  completed  the  print  may 
be  developed  by  immersing  in  a  tank  of  clear  water,  face  up. 
Lave  the  water  over  the  face  of  the  print  a  few  times  with  the 
hand  and  then  hang  up  to  dry. 

When  dry  the  print  should  be  trimmed  to  the  exact  size  of 
the  drawing  plate,  in  this  case  i5"X2o". 

PLATE  18 

This  plate  is  to  consist  of  one  or  more  of  the  following  prob- 
lems and  is  to  be  drawn  in  pencil  first  according  to  the  directions 
given  in  Art.  84,  and  when  approved  is  to  be  traced  in  ink 
on  the  dull  side  of  tracing  cloth. 

A  tracing  in  ink  should  be  begun  by  inking  first  the  small 
arcs  of  circles  with  the  spring  bow  pen,  then  the  larger  arcs  and 


WORKING  DRAWINGS 


149 


circles  with  the  compass  pen  and  all  irregular  curves  with  the 
French  curve,  after  which  the  straight  lines  should  be  inked 
with  the  straight  line  pen  and  the  figures  and  lettering  with  the 
writing  pen,  ball-point  No.  516. 

PROB.  79,  FIG.  162.  Draw  a  front  view  and  plan  of  the  con- 
necting rod  shown  in  Fig.  162.  Scale:  3"  =  !'.  See  Fig.  146. 

ist.  Begin  by  drawing  the  H  center  line  of  the  plan  i|" 
below  the  top  border  line  and  the  H  center  line  of  the  elevation 
3J"  below  the  center  line  of  the  plan. 

2d.  Draw  the  V  center  line  through  the  center  of  the  crank 
pin  circle  shown  in  adjacent  part  lines,  and  the  V  center  line 


FIG.  162. 

through  the  center  of  the  crosshead  pin  circle  also  shown  in 
adjacent  part  line  at  the  right-hand  end  of  the  connecting  rod. 

4th.  Lay  off  the  widths  and  lengths  of  the  left  stub  end  and 
then  of  the  right-hand  stub  end  according  to  the  dimensions  given. 

5th.  To  determine  the  slope  of  the  rod  body.  The  plate  is 
not  long  enough  to  draw  the  rod  to  its  true  length  so  it  is  broken 
in  the  middle  as  shown. 

From  the  8|"  line  at  the  left-hand  end  of  the  rod  body  lay 
off  3  ft.  6f "  to  the  right  on  center  line  at  that  point  draw  a  per- 
pendicular line  intersecting  the  center  line  of  the  rod  and  lay 
off  3"  on  each  side  of  the  center  line  and  draw  the  taper  rod 
through  the  8^  and  6"  points  as  long  as  shown  to  the  break. 

6th.  Repeat  the  process  to  the  left  for  the  right-hand  taper. 
Study  carefully  Art.  84  for  the  detail  methods  to  be  used  in 
making  the  complete  pencil  drawing  tracing  and  blue  print. 


150 


MECHANICAL  DRAWING 


PROB.  80.     Make  the  V,  H  and  Pr  projections  of  the  Engine 
Link  Support  given  in  the  isometric  drawing,  Fig.  163      Scale: 

i  st.  Lay  out  all  the  V,  H  and  P  center  lines  in  convenient 
positions  on  the  plate. 

2d.  Arrange  position  of  V  section  indicated  on  Fig.  163. 


FIG.  163. 


3d.  Follow  instructions  given  in  Art.  84  for  the  proper 
completion  of  the  drawing. 

Indicate  finished  surfaces  as  directed  in  Art.  29. 

PROB.  81.  Given  the  elevation  and  plan  of  the  planer  Top 
Bracket,  Fig.  164.  Draw  also  the  end  view,  omitting  all  hidden  lines. 
Scale  6"  =  i'. 


WORKING  DRAWINGS 


151 


Fig.  165  is  the  isometric  of  the  Top  Bracket. 
NOTE:  The  2"  and  if  circles  are  to  be  drawn  on  the  same 
center  line  with  the  upright  arm,  which  is  if"  wide.     Fig.  163. 


FIG.  164. 


FIG.  165. 


PROB.  82.  Draw  the  Engine  Axle  shown  in  Fig.  166.  Make 
cross-sections  as  shown.  Material  cold  rolled  steel  (C.R.S.)  Scale: 
6"  =  i'. 


FIG.  i 66. 

PROB.  83.  Given  the  V  and  P  projection  oj  the  automobile  axle 
shown  in  Fig.  167,  draw  also  a  plan  of  the  top.  Scale:  3"  =  i'. 

i  st.  Lay  out  center  lines  of  the  V  and  P  projections  shown  in 
Fig.  167,  locating  them  so  as  to  allow  for  plan  above  elevation. 

2d.  Draw  center  line  of  plan  i  J"  below  upper  border  line. 

3d.  Make  the  drawing  of  the  elevation  around  the  center  lines. 

4th.  Draw  the  end  views  similar  to  those  shown,  making 
improvements  where  possible. 

5th.  Draw  plan  from  elevation  and  end  view. 

6th.  When  complete  in  fine  pencil  lines  submit  for  approval. 

7th.  When  approved  in  fine  lines,  clean,  strengthen  and  place 
dimension  lines,  dimensions,  notes  and  title  according  to  previous 
directions. 


152 


MECHANICAL  DRAWING 


85.  Title  Sheet  or  Set  of  Drawings.  When  all  the  draw- 
ings of  the  course  in  mechanical  drawing  have  been  completed 
they  should  be  placed  together  in  the  order  of  their  making  with 


•H 

n, 

1 

i 

u 

•F- 

i 

\ 

. 

\ 

-o: 

• 

- 

1 

o 

\ 

§  b4 

rr      ,    § 

Irt 


Jlj 


M' 


first  drawing  on  top  and  taken  to  the  instructor  to  be  checked  up 
with  the  records  to  see  that  due  credit  has  been  given  for  each 
drawing. 


WORKING  DRAWINGS  153 

The  drawings  should  then  be  bound  together  with  a  cover 
plate  design  appropriately  lettered. 

This  cover  plate  is  to  be  placed  on  top  of  the  drawings  and 
the  whole  fastened  with  brass  paper  binders. 

^COVER  PLATE  DESIGN 

The  general  style  and  layout  of  the  lettering  is  left  to  the 
taste  of  the  student  except  that  the  main  title  "  Mechanical 
Drawing  "  is  to  be  made  with  the  Roman  letter,  all  capitals, 
shown  in  Fig.  1 73  of  the  Appendix,  page  1 58. 


FREEHAND      LETTER  ING 


MECHANICAL  DRAWING 

^PLATES  I  n*22  INCLUSIVE 

••57VRMOUR     INSTITUTE  ocfTECMNOLOOY 


CHICAOp.  U.U 


nn 


FIG.  168. 


Fig.  1 68  gives  a  sample  title  plate  showing  the  heights  of 
letters  of  the  different  lines. 

Figs.  169  to  172  inclusive  are  suggestive  designs,  but  the 
student  is  urged  to  make  his  cover  plate  with  a  design  of  his 
own  as  far  as  possible. 


154 


MECHANICAL  DRAWING^ 


FREEHAND  LETTERING 


AND 


MECHANICAL  DRAWING 


PLAT 


E5    I  TO 


^2  I 


c 


ARMOUR  INSTITUTE  OF  TECHNOLOGY 

CHICAGO  -  MAR.  15. 19)8 .  C  PFEIFFta 


FlG.   169. 


FREEHAND  LETTERING 

AND 


MECHANICAL     DRAWING 


1 1»  22  INCL 


PLATES 


ARMOUR    INSTITUTE  <*  TECHNOLOGY 

CHICAGO  -APRIL  12  1918  A  G  FALK 


FIG.  170. 


WORKING  DRAWINGS 


155 


FREEHAND  LETTERING 

AND 


MECHANICAL     DRAWING 


rLAtos  /TO 


ARMOUR 


OT 


FIG.  171. 


FREEHAND     LETTERING 
AND 

MECHANICAL  DRAWING 


ARMOUR    INSTITUTE  OF  TECHNOLOGY 

PLATES   16-22  CHICAGO,   ILL 


FIG.  172. 


APPENDIX 

TO  THE 

REQUIRED   COURSE   IN    MECHANICAL  DRAWING 


86.  Lettering  Continued.  While  it  is  true  that  the  Gothic 
letter,  all  capitals,  sloping  and  equal  in  height  is  the  preferred 
letter  for  notes  and  titles  on  commercial  drawings,  there  are  a 
few  other  styles  that  are  sometimes  used  on  special  drawings. 

FIG.  173  is  a  carefully  proportional  Roman  letter  that  is  often 
used  for  titles  of  outside  cover  plates,  etc.  This  letter  is  difficult 
to  make  well  freehand,  but  when  made  mechanically  according 
to  the  proportions  given  in  Fig.  173,  it  presents  a  fine  appearance 
and  can  be  used  in  conjunction  with  other  styles.  See  Art.  85 
on  cover  plates,  page  152. 

FIG.  174  shows  the  lower  case  Roman  letter.  This  letter  is 
not  much  used  in  machine  drawing. 

FIG.  175  shows  the  upper-  and  lower-case  letters  of  a  vertical 
Gothic  that  is  sometimes  used. 

FIGS.  176  and  177  give  a  style  of  letter  much  used  by  archi- 
tects both  for  titles  and  notes  on  drawings. 

More  latitude  is  allowed  to  the  architectural  draftsman  in 
his  choice  of  styles  of  lettering  for  notes  and  titles  on  working 
drawings  than  is  given  to  the  machine  draftsman.  The  latter 
is  required  to  use  that  style  of  letter  which  gives  the  neatest  ap- 
pearance with  a  maximum  of  legibility  and  requires  the  least 
amount  of  labor  and  time  to  construct  it;  while  the  former  is 
expected  to  use  a  style  of  letter  suggested  by  the  character  of 
the  drawing  to  be  named  and  noted. 

157 


158 


MECHANICAL  DRAWING 


r 


APPENDIX  TO  THE  REQUIRED  COURSE 


159 


itt 


1 


m 


w 


160 


MECHANICAL  DRAWING 


APPENDIX  TO  THE  REQUIRED  COURSE 


161 


The  alphabet  shown  in  Figs.  176  and  177,  known  as  the  classic 
Renaissance  letters,  is  selected  as  a  good  form  of  letter  for  general 
purposes,  where  a  Roman  letter  would  be  suitable  for  the  work 
in  hand.  This  alphabet  was  originally  designed  by  Albrecht 


FIG.  176. 

Diirer  and  adopted  by  Frank  Chouteau  Brown,  in  his  treatise 
on  "  Letters  and  Lettering,"  Bates  &  Guild  Company,  Boston. 
Mr.  Brown's  book  is  recommended  to  those  students  who  desire 
to  follow  up  their  studies  in  architectural  lettering. 


162 


MECHANICAL  DRAWING 


FIG.  177. 


APPENDIX  TO  THE  REQUIRED  COURSE  163 


i8-Point  Roman. 


ABCDEFGHIJKLMN  OPQRSTUV  WX 
YZ      abcdefghijklmnopqrstuvwxyz 
1234567890 


i8-Point  Italic. 


AB  CDEFGHIJKLMNOP  QBSTUV 
WXYZ    abcdefghijklmnopqrstuvwxyz 

I?.- Point  Cushing  Italic. 

ABCDEFGHIJKLMNOPQRSTUVWXYZ       abcdefehijklm 
nopqrsiuvwxyz         1234567890 


28-Point  Boldface  Italic. 


ABCDEFGHIJKLM 
NOPQRSTUVWXYZ 

abcdefghijklmnopqrstu 
vwxyz    1234567890 

Two-Line  Nonpareil  Gothic  Condensed. 

ABCDEFGHIJKLMNOPQRSTUVWXYZ      1234567890 

Three-Line  Nonpareil  Lightface  Celtic. 

ABCDEFGHIJKLMNOPQR 
STUVAVXYZ        abedefghijkl 
mnopqrstu  vwxyz 
1234567890 " 


164  MECHANICAL  DRAWING 


1 8- Point  Chelsea  Circular. 


ABCDEFGHIJKLMNOPQRSTUVWX 

YZ     abcdefgh\ij^lmr(Opqrstuvwxyz 

1234567890 

i8-Point  Elandkay. 

flBCDEFGHUKLMNOPQRSTUWXYZ 

1 234567890 

i8-Point  Quaint  Open. 
28-Point  Roman. 

ABCDEFGHIJKLM 
NOPQRSTUVWXYZ 

abcdefghijklmnopqrstu 
vwxyz    123456T89O 


zS-Point  Old-Style  Italic. 


ABCDEFGHIJKLMNOP 

QRSTUyWXYZ     abcdefg 
hijklmnopqrstuvwxyz 
1234567890 


APPENDIX  TO  THE  REQUIRED  COURSE  16$ 

iz-Point  Victoria  Italic. 

I          ABCDEFCHIJKLMNOPQRSTU 

YWXYZ      1234567890 

\ 

:-  iS-Point  DeVinne  Italic. 

ABCDEPGHIJKLMNOPQRSTU 

VWXYZ    abcdefghijklmnopqrst 

uvwxyz    1234567890 

22-Point  Gothic  Italic. 

ABCDEFGHIJKLMNOPQRSTUVMYZ 

I         t      abcdefghijklmnopqrstuuwxyz 

1234567890 

Double- Pica  Program. 

ABCDEFGHIJKLMNO 

PQRSTUYWXYZ 
I      abcdefghijklmnopqrstuv 
I       wxyz   1234567890 

Nonpareil  Telescopic  Gothic. 

ABCDEFGHUKLMNOPQRSTUVWXYZ         1284567890 


166 


MECHANICAL  DRAWING 


24-Point  Gallican. 


ABCDEFGHIJKL 
MNOPQRSTUVW 
XYZ  1234567890 


Two-Line  Virile  Open. 


22-Point  Old-Style  Roman. 


ABCDEFGHIJKLMNOPQRST 

UVWXYZ      abcdefghijklmnopqrst 

uvwxyz,      1234567890 


36-Point  Yonkers. 


^25^567890 


APPENDIX  TO  THE  REQUIRED  COURSE 


167 


The  method  used  for  the  instrumental  construction  of  these, 
letters  is  similar  to  that  used  in  the  Roman  letter  given  on 
page  158. 

For  the  purpose  of  learning  the  form  and  proportions  of  these 
letters  the  alphabet  should  be  drawn  mechanically  to  a  scale  as 
large  as  convenient;  after  which  practice  should  be  had  by  form- 
ing the  letters  freehand  to  small  sizes,  until  the  student  becomes 
familiar  with  their  construction. 

In  the  following  pages  a  number  of  type  specimens  are  given 
that  students  may  have  a  choice  when  some  special  lettering  is 
desired. 

"36-point  Yonkers  "  on  page  166  is  sometimes  used  in  special 
work.  It  is  easy  to  construct  with  F.  Soenneckin's  round  writing- 
pens,  single  point  or  the  automatic  shading-pen.  But  it  lacks 
legibility  and  is  therefore  not  much  used. 

87.  Geometrical  Drawing  Continued.  Among  the  following 
problems  given  here,  in  addition  to  the  regular  course,  many 
of  them  are  of  practical  value  in  drafting  as  well  as  being  good 
exercises  in  drawi  g. 

FIG.  178.  To  Erect  a  Perpendicular  at  the  End  of  the  Line. 
Assume  the  point  E  above  the  line  as  center  and  radius  EB, 
describe  an  arc  CBD,  cutting  the  line  AB  in  the  point  C.  From 
C  draw  a  line  through  E}  cutting  the  arc  in  D.  Draw  DB  the 
perpendicular. 


FIG.  178. 

FIG.  179.  The   Same   Problem:    A    Second   Method.    With 
center  B  and  any  radius  as  BC  describe  an  arc  CDE  with  the 


168 


MECHANICAL  DRAWING 


same  radius;  measure  off  the  arcs  CD  and  DE.     With  D  and  E 
as  centers  and  any  convenient  radius  describe  arcs  intersecting 
at  F.     FB  is  the  required  perpendicular. 
F 


FIG.  1 80.  To  Draw  a  Perpendicular  to  a  Line  from  a  Point 
above  or  below  It.  Assume  the  point  C  above  the  line.  With 
center  C  and  any  suitable  radius  cut  the  line  AB  in  E  and  F. 
From  E  and  F  describe  arcs  cutting  in  D.  Draw  CD  the  per- 
pendicular required. 

FIG.  181.  To  Draw  a  Line  Parallel  to  a  Given  Line  AB 
through  a  Given  Point  C.  From  any  point  on  AB  as  B  with 
radius  BC  describe  an  arc  cutting  AB  in  A.  From  C  with  the 
same  radius  describe  arc  BD.  From  B  with  AC  as  radius  cut 
arc  BD  in  D.  Draw  CD.  Line  CD  is  parallel  to  AB. 


FIG.  181. 

FIG.  182.  To  Divide  a  Line  AB  Proportionally  to  the  Divided 
Line  CD.    Draw  AB  parallel  to  CD  at  any  points  5,  6,  7,  8,  etc. 


APPENDIX  TO  THE  REQUIRED  COURSE 


169 


The  divisions  on  AB  will  have  the  same  proportion  to  the 
divisions  on  CD  that  the  whole  line  AB  has  to  the  whole  line 
CD,  i.e.,  the  lines  will  be  proportionally  divided. 


FIG.  183.  The  Same:  Another  Method.  Let  BC,  the  divided 
line,  make  any  angle  with  BA ,  the  line  to  be  divided  at  B.  Draw 
line  CA  joining  the  two  ends  of  the  lines.  Draw  lines  from  5,  6,  7, 
8,  parallel  to  CA,  dividing  line  AB  in  points  i,  2,  3,  4,  propor- 
tional to  BC. 

FIG.  184.  To  Construct  a  Square,  its  Base  AB  being  Given. 
Erect  a  perpendicular  at  B.  Make  BC  equal  to  AB.  From  A 
and  C  with  radius  AB  describe  arcs  cutting  in  D.  Join  DC  and 
DA. 

A 


' B 


FIG.  184. 


FIG.  185. 


FIG.  185.  To  Construct  a  Square  Given  Its  Diagonal  AB. 
Bisect  AB  in  C.  Draw  DF  perpendicular  to  AB  at  C.  Make 
CD  and  CF  each  equal  to  CA .  Join  AD,  DB,  BF  and  FA . 


170 


MECHANICAL  DRAWING 


FIG.  1 86.  To  Construct  a  Regular  Polygon  of  Any  Number  of 
Sides  given  the  Circumscribing  Circle.  Draw  a  diameter  AB  of 
the  given  circle.  Divide  AB  into  as  many  equal  parts  as  the 
polygon  is  to  have  sides,  say  5.  From  A  and  B  with  the  line  AB 
as  radius  describe  arcs  cutting  in  C,  draw  a  line  from  C  through 
the  second  division  of  the  diameter  and  produce  it  cutting  the 
circle  in  D.  BD  will  be  the  side  of  the  required  polygon.  The 
line  C  must  always  be  drawn  through  the  second  division  of  the 
diameter,  whatever  the  number  of  sides  of  the  polygon. 


FIG.  187.  To  Construct  any  Regular  Polygon  with  a  Given  Side 
AB.  Make  BD  perpendicular  and  equal  to  AB.  With  B  as 
center  and  radius  AB  describe  arc  DA.  Divide  arc  DA  into  as 
many  equal  parts  as  there  are  sides  in  the  required  polygon,  as 
i,  2,  3,  4,  5.  Draw  B2.  Bisect  line  AB  and  erect  a  perpendicular 
at  the  bisection,  cutting  B  2in  C.  With  C  as  center  and  radius 
CB  describe  a  circle.  With  AB  as  a  chord  step  off  the  remaining 
sides  of  the  polygon. 

FIG.  188.  Another  Method.  Extend  line  AB.  With  center 
A  and  any  convenient  radius  describe  a  semicircle.  Divide  the 
semicircle  into  as  many  equal  parts  as  there  are  sides  in  the 
required  polygon,  say  6.  Draw  lines  through  every  division 
except  the  first.  With  A  as  center  and  AB  as  radius  cut  off  A 2 


APPENDIX  TO  THE  REQUIRED  COURSE 


171 


in  C.     From  C  with  the  same  radius  cut  A$  in  D.     From  D, 
A4mE.     From  B,  AS  in  F.    Join  AC,  CD,  DE,  EF,  and  FB. 


FIG.  187. 


FIG.  1 88. 


FIG.  189.  To  Construct  a  Regular  Heptagon,  the  Circum- 
scribing Circle  being  Given.  Draw  a  radius  AB.  With  B  as 
center  and  BA  as  radius,  cut  the  circumference  in  i ,  2 ;  it  will  be 
bisected  by  the  radius  in  C.  Ci  or  €2  is  equal  to  the  side  of  the 
required  heptagon. 


FIG.  189. 


FIG.  190.  To  Construct  a  Regular  Octagon,  the  Circumscribing 
Circle  being  Given.  Draw  a  diameter  AB.  Bisect  the  arcs  AB 
in  C  and  D.  Bisect  arcs  CA  and  CB  in  i  and  2.  Draw  lines 


172 


MECHANICAL  DRAWING 


from  i  and  2  through  the  center  of  the  circle,  cutting  the  cir- 
cumference in  3  and  4.     Join  Ai,  iC,  C2,  2$,  B$,  etc. 

FIG.  191.  To  Inscribe  an  Octagon  in  a  Given  Square.  Draw 
diagonals  AD,  CB  intersecting  at  O.  From  A,  B,  C,  and  D  with 
radius  equal  to  AO  describe  quadrants  cutting  the  sides  of  the 
square  in  i,  2,  3,  4,  5,  6,  7,  8.  Join  these  points  and  the  octagon 
will  be  inscribed. 

C  6 


FIG.  i 91. 

FIG.  192.  To  Find  a  Fourth  Proportional  to  Three  Given  Right 
Lines  AB,  CD,  and  EF.  Make  GH=  the  given  line  AB.  Draw 
GI  =  CD,  making  any  convenient  angle  to  Gil.  Join  HI .  From 
G  lay  off  GK  =  EF.  From  K  draw  a  parallel  to  HI  cutting  GI  in 
L.  GL  is  the  fourth  proportional  required. 

II 


F 
FIG.  192. 


FIG.  193. 


FIG.  193.  To  Draw  a  Line  Tangent  to  an  Arc  oj  a  Circle. 
(ist)  When  the  center  is  not  accessible.    Let  B  be  the  point 


APPENDIX  TO  THE  REQUIRED  COURSE 


173 


through  which  the  tangent  is  to  be  drawn.  From  B  lay  off  equal 
distances  as  BE,  BF.  Join  EF  and  through  B  draw  ABC  par- 
allel to  EF.  (2d)  When  the  center  D  is  given.  Draw  BD  and 
through  B  draw  ABC  perpendicular  to  BD.  ABC  is  tangent 
to  the  circle  at  the  point  B. 

FIG.  194.  To  Draw  Tangents  to  the  Circle  C  from  the  Point  A 
Without  It.  Draw  AC  and  bisect  it  in  E.  From  E  with  radius 
EC  describe  an  arc  cutting  circle  C  in  B  and  D.  Join  CB}  CD. 
Draw  AB  and  AD  tangent  to  the  circle  C. 


FIG.  194. 


FIG.  195. 


FIG.  195.  To  Draw  a  Tangent  between  Two  Circles.  Join  the 
centers  A  and  B.  Draw  any  radial  line  from  A  as  A  2  and  make 
1-2  =  the  radius  of  circle  B.  From  A  with  radius  A-2  describe  a 
circle  CiD.  From  center  B  draw  tangents  BC  and  BD  to  circle 
CzD  at  the  points  C  and  D  by  preceding  problem.  Jcin  AC  and 
AD  and  through  the  points  E  and  F  draw  parallels  FG  and  jEfl" 
to  BD  and  £C.  FG  and  EH  are  the  tangents  required. 

FIG.  196.  To  Draw  Tangents  to  Two  Given  Circles  A  and  B. 
Join  A  and  B.  From  A  with  a  radius  equal  to  the  difference  of 
the  radii  of  the  given  circles  describe  a  circle  CF,  From  B  draw 


174 


MECHANICAL  DRAWING 


the  tangents  BF  and  BG,  by  Prob.  37.  Draw  AF  and  AG 
extended  to  E  and  H.  Through  E  and  H  draw  EC  and  HD  par- 
allel to  BF  and  .£G  respectively.  EC  and  £>#  are  the  tangents 
required. 


FIG.  IQ(». 


FIG.  197. 


FIG.  197.  To  Draw  an  Arc  of  a  Circle  of  Given  Radius  Tangent 
to  Two  Straight  Lines.  AB  and  AC  are  the  two  straight  lines, 
and  r  the  given  radius.  At  a  distance  =  r  draw  parallels  1-2  and 

I  R 


3-4  to  AC  and  AB,  intersecting  at  F.  From  F  draw  perpendic- 
ulars FD  and  FE.  With  F  as  center  and  FD  or  FE  as  radius 
describe  the  required  arc,  which  will  be  tangent  to  the  two  straight 
Jines  at  the  points  D  and  E, 


APPENDIX  TO  THE  REQUIRED  COURSE 


175 


FIG.  198.  To  Inscribe  a  Circle  within  a  Triangle  ABC.  Bisect 
the  angles  A  and  B.  The  bisectors  will  meet  in  D.  Draw  Di 
perpendicular  to  AB.  Then  with  center  D  and  radius  =  Z)i  de- 
scribe a  circle  which  will  be  tangent  to  the  given  triangle  at  the 
points  i,  2,  3. 

FIG.  199.  To  Draw  an  Arc  of  a  Circle  of  Given  Radius  R  Tan- 
gent to  Two  Given  Circles  A  and  B  'when  the  A  re  Includes  One  Circle 
and  Excludes  the  Other.  Through  A  draw  any  diameter  and  make 
1-2 = R.  From  B  draw  any  radius  and  extend  it,  making  3-4 =R. 


FIG.  199. 

With  center  A  and  radius  A  2  and  center  B  and  radius  £4  describe 
arcs  cutting  at  C.  With  C  as  center  and  radius  =  C5  or  C6 
describe  the  arc  5,  6. 

FIG.  200.  Draw  an  Arc  of  a  Circle  of  Given  Radius  R  Tangent 
to  a  Straight  Line  AB  and  a  Circle  CD.  From  E,  the  center  of 
the  given  circle,  draw  an  arc  of  a  circle  i,  2  concentric  with  CD  at 
a  distance  R  from  it,  and  also  a  straight  line  3,  4  parallel  to  AB 
at  the  same  distance  R  from  AB.  Draw  EO  intersecting  CD  at 
5.  Draw  the  perpendicular  06.  With  center  0  and  radius  06 
or  05  describe  the  required  arc. 

FIG.  201.  To  Describe  an  Ellipse  Approximately  by  Means  of 
Three  Radii.  (F.  R.  Honey's  method.)  Draw  straight  lines 


176 


MECHANICAL  DRAWING 


RH  and  HQ,  making  any  convenient  angle  at  H.  With  center  H 
and  radii  equal  to  the  semi-minor  and  semi-major  axes  respec- 
tively, describe  arcs  LM  and  NO.  Join  LO  and  draw  MK  and 
NP  parallel  to  LO.  Lay  off  Li  =  f  of  LN.  Join  Oi  and  draw 

9 
A  6  B 


FIG.  200. 


M2  and  N$  parallel  to  Oi.  Take  #3  for  the  longest  radius 
(  =  r),  #2  for  the  shortest  radius  (=£),  and  one-half  the  sum 
of  the  semi-axes  for  the  third  radius  (  =  S)  ,  and  use  these  radii  to. 
describe  the  ellipse  as  follows:  Let  AB  and  CD  be  the  major 


FIG.  201. 

and  minor  axes.  Lay  off  A^  =  E  and  A$=S.  Then  lay  off  CG 
=  T  and  C6=S.  With  G  as  center  and  G6  as  radius  draw  the 
arc  6,  g.  With  center  4  and  radius  4,  5,  draw  arc  5,  g,  intersect- 
ing 6,  g  at  g.  Draw  the  line  <7g  and  produce  it  making  GS  =  T, 


APPENDIX  TO  THE  REQUIRED  COURSE 


177 


Draw  g,  4  and  extend  it  to  7  making  g,  J=S.  With  center  G  and 
radius  GC(  =  T)  draw  the  arc  C8.  With  center  g  and  radius 
g,  8  (  =  5)  draw  the  arc  8,  7.  With  center  4  and  radius  4,  7 
(=£)  draw  arc  jA.  The  remaining  quadrants  can  be  drawn 
in  the  same  way. 

FIG.  202.  To  Describe  an  Ellipse  Given  the  Semi-axes  AB  and 
CD.  Let  AB  and  AC  be  the  semi-axes.  With  A  as  center  and 
radii  AB  and  AC  describe  circles.  Draw  any  radii  as  A$  and  Aq, 
etc.  Make  31,42,  etc.,  perpendicular  to  AB,  and  Z>2,  £5,  etc., 
parallel  to  AB.  Then  i,  2,  5,  etc.,  are  points  on  the  curve. 

FIG.  203.  Another  Method.  Place  the  diameters  as  before, 
and  construct  the  rectangle  CDEF.  Divide  AB  and  DB  and  BF 
into  the  same  number  of  equal  parts  as  i?  2,  3,  and  B.  Draw 


from  C  through  points  i,  2,  3  on  AB  and  BD  lines  to  meet  others 
drawn  from  E  through  points  i,  2,  3  on  AB  and  FB  intersecting 
in  points  GHK.  GHK  are  points  on  the  curve. 

FIG.  204.  To  Construct  a  Parabola,  the  Base  CD  and  the 
Abscissa  AB  Being  Given.  Draw  EF  through  A  parallel  to  CD 
and  CE  and  DF  parallel  to  AB.  Divide  AE,  AF,  EC,  and  FD 
into  the  same  number  of  equal  parts.  Through  the  points  i,  2,  3 
on  AF  and  AE  draw  lines  parallel  to  A  V,  and  through  A  draw 
lines  to  the  points  i,  2,  3  on  FD  and  EC  intersecting  the  parallel 
lines  in  points  4,  5,  6,  etc.,  of  the  curve. 

FIG.  205.  Given  an  Ellipse  to  Find  the  Axes  and  Foci.  Draw 
two  parallel  chords  AB  and  CD.  Bisect  each  of  these  in  E  and  F. 
Draw  EF  touching  the  ellipse  in  i  and  2.  This  line  divides  the 
ellipse  obliquely  into  equal  parts.  Bisect  i,  2  in  G,  which  will 


178 


MECHANICAL  DRAWING 


be  the  center  of  the  ellipse.  From  G  with  any  radius  draw  a 
circle  cutting  the  ellipse  in  HIJK.  Join  these  four  points  and  a 
rectangle  will  be  formed  in  the  ellipse.  Lines  LM  and  NO, 
bisecting  the  sides  of  the  rectangle,  will  be  the  diameters  or  axes 
of  the  ellipse.  With  N  or  0  as  centers  and  radius  =  GL  the  semi- 
major  axis,  describe  arcs  cutting  the  major  axis  in  P  and  Q  the 
foci. 

FIG.  206.  To  Construct  a  Spiral  of  One  Revolution.    Describe 
a  circle  using  the  widest  limit  of  the  spiral  as  a  radius.     Divide 

A 


the  circle  into  any  number  of  equal  parts  as  A ,  B,  C,  etc.  Divide 
the  radius  into  the  same  number  of  equal  parts  as  i  to  12.  From 
the  center  with  radius  12,  i  describe  an  arc  cutting  the  radial 
line  B  in  i'.  From  the  center  continue  to  draw  arcs  from  points 


APPENDIX  TO  THE  REQUIRED  COURSE 


179 


2,  3,  4,  etc.,  cutting  the  corresponding  radii  C,  D,  E,  etc.,  in  the 
points  2' ',  3',  4',  etc.  From  12  trace  the  Archimedes  Spiral  of 
one  revolution. 

Fig.  207.  To  Describe  a  Spiral  of  any  Number  cf  Revolutions, 
e.g.,  2.  Divide  the  circle  into  any  number  of  equa)  parts  as  A,  B, 
C,  etc.,  and  draw  radii.  Divide  the  radius  A 12  into  a  number 
of  equal  parts  corresponding  with  the  required  number  of  revo- 
lutions and  divide  these  into  the  same  number  of  equal  parts  as 
there  are  radii,  viz.,  i  to  12.  It  will  be  evident  that  the  figure 
consists  of  two  separate  spirals,  one  from  the  center  of  the  circle 
to  12,  and  one  from  12  to  A.  Commence  as  in  the  last  prob- 
lem, drawing  arcs  from  i,  2,  3,  etc.,  to  the  correspondingly 
numbered  radii,  thus  obtaining  the  points  marked  i',  2',  3',  etc. 
The  first  revolution  completed,  proceed  in  the  same  manner  to 
find  the  points  i",  2",  3",  etc.  Through  these  points  trace  the 
spiral  of  two  revolutions. 

Fig.  208.  To  Describe  the  Cycloid.  AB  is  the  director,  CB  the 
generating  circle,  X  a  piece  of  thin  transparent  celluloid,  with 


FIG.  208. 


FIG.  209. 


one  side  dull  on  which  to  draw  the  circle  C.  At  any  point  on  the 
circle  C  puncture  a  small  hole  with  a  sharp  needle,  and  place  the 
point  C  tangent  to  the  director  AB  at  the  point  from  which  the 
curve  is  to  be  drawn.  Hold  the  celluloid  at  this  point  with  a 
needle,  and  rotate  it  until  the  arc  of  the  circle  C  intersects  the 
director  AB.  Through  the  point  of  intersection  stick  another 
needle  and  rotate  X  until  the  circle  is  again  tangent  to  AB,  and 
through  the  puncture  at  C  with  a  4H  pencil,  sharpened  to  a  fine 
conical  point,  mark  the  first  point  on  the  curve.  So  proceed 
until  sufficient  points  have  been  found  to  complete  the  curve. 


180 


MECHANICAL  DRAWING 


(NOTE. — The  thin  celluloid  was  first  used  as  a  drawing  in- 
strument by  Professor  H.  D.  Williams,  of  Sibley  College,  Cornell 
University.) 

FIG.  209.  To  Find  the  Length  of  a  Given  Arc  of  a  Circle 
Approximately.  Let  BC  be  the  given  arc.  Draw  its  chord  and 
produce  it  to  A ,  making  BA  equal  half  the  chord.  With  center 
A  and  radius  AC  describe  arc  CD  cutting  the  tangent  line  BD 
at  D,  and  making  it  equal  to  the  arc  BC. 

FIG.  210.  To  Describe  the  Cycloid  by  the  Old  Method.  Divide 
the  director  and  the  generating  circle  into  the  same  number  of 


FIG.  210. 


equal  parts.  Through  the  center  a  draw  ag  parallel  to  AB  for 
the  line  of  centers,  and  divide  it  as  AB  in  the  points  b,  c,  d,  e,  /, 
and  g.  With  centers/,  e,  d,  etc.,  describe  arcs  tangent  to  AB, 
and  through  the  points  of  division  on  the  generating  circle  i,  2,  3, 
etc.,  draw  lines  parallel  to  AB  cutting  the  arcs  in  the  points  i', 
2',  3',  etc.  These  will  be  points  in  the  curve. 

An  approximate  curve  may  be  drawn  by  arcs  of  circles. 
Thus,  taking/  as  center  and/g'  as  radius,  draw  arc  gV.  Pro- 
duce I'f  and  2fe'  until  they  meet  at  the  center  of  the  second 
arc  2'/',  etc. 

FIG.  211.  Another  Method.  Draw  the  generating  circle  on 
the  celluloid  and  roll  it  on  the  outside  of  the  director  BC  for  the 
Epicycloid,  and  on  the  inside  for  the  Hypocycloid. 

FIG.  212.  To  Draw  the  Cissoid.  Draw  any  line  AB  and  BC 
perpendicular  to  it.  On  BC  describe  a  circle.  From  the  extrem- 


APPENDIX  TO  THE  REQUIRED  COURSE 


181 


ity  C  of  the  diameter  draw  any  number  of  lines,  at  any  distance 
apart,  passing  through  the  circle  and  meeting  the  line  AB  in 
i',  2',  3',  etc.  Take  the  length  from  A  to  9  and  set  it  off  from  C 
on  the  same  line  to  g"  '.  Take  the  distance  from  8'  and  set  it 
off  from  C  on  the  same  line  to  8",  etc.,  for  the  other  divisions, 
and  through  9",  8",  7",  6",  etc.,  draw  the  curve. 


FIG.  211. 


FIG.  212. 


FIG.  213.  To  Draw  Schiele's  Anti-friction  Curve.  Let  AB 
be  the  radius  of  the  shaft  and  Bi,  2,  3,  4,  etc.,  its  axis.  Set  off 
the  radius  AB  on  the  straight  edge  of  a  piece  of  stiff  paper  or 
thin  celluloid  and  placing  the  point  B  on  the  division  i,  of  the 
axis,  draw  through  point  A  the  line  A  i  .  Then  lower  the  straight 
edge  until  the  point  B  coincides  with  2  and  the  point  A  just 
touches  the  last  line  drawn,  and  draw  <Z2,  and  so  proceed  to  find 
the  points  a,  b,  c,  etc.  Through  these  points  draw  the  curve. 


182 


MECHANICAL  DRAWING 


FIG.  214.  To  Describe  an  Interior  Epicycloid.  Let  the  large 
circle  X  be  the  generator  and  the  small  circle  Y  the  director. 
Divide  circle  Y  into  any  number  of  equal  parts,  as  B,  H,  /,  /,  etc. 
Draw  radial  lines  and  make  HC,  ID,  JE,  KF,  etc.,  each  equal  to 
the  radius  of  the  generator  X.  With  centers  C,  D,  E,  etc., 
describe  arcs  tangent  at  H,  I,  /,  etc.  Make  Hi  equal  to  one  of 
the  divisions  of  the  director  as  BE.  Make  /2  equal  to  two 
divisions,  /3,  three  divisions,  etc.,  and  draw  the  curve  through 
the  points  i,  2,  3,  4. 


FIG.  213. 


214. 


FIG.  215.  To  Construct  a  Scale  of  Sixth  Size  or  2"-=!  Foot. 
Draw  upon  a  piece  of  tough  white  drawing-paper  two  parallel 
lines  about  i"  apart  and  about  14"  long  as  shown  by  a,  Fig.  98. 
From  A  lay  off  distances  equal  to  2"  and  divide  the  first  space 
AB  into  12  equal  parts  or  inches  by  Prob.  12.  Divide  AE  in 
the  same  way  into  as  many  parts  as  it  may  be  desired  to  sub- 
divide the  inch  divisions  on  AB,  usually  8.  When  the  divisions 
and  subdivisions  have  been  carefully  and  lightly  drawn  in  pencil 
as  shown  by  a,  in  Fig.  215,  then  the  lines  denoting  f",  J" ',  J" ',  i", 
and  3"  should  be  carefully  inked  and  numbered  as  shown  by  (b). 
By  a  further  subdivision  a  scale  of  i"  =  i  foot  may  easily  be  made 
as  shown  by  (c)  in  Fig.  215. 

FIGS.  216  and  217.  Draw  the  projections  of  a  circular  plane 
(i)  when  its  surface  is  parallel  to  the  vertical  plane,  (2)  when  it 


APPENDIX  TO  THE  REQUIRED  COURSE 


183 


makes  an  angle  of  45°  with  the  V.P.,  and  (3)  when  still  making 
an  angle  of  45°  with  the  V.P.  it  has  been  revolved  through  an 
angle  of  60°. 

First  position:    Draw  the  circular   plane  ic,  2",  3°,  4",  etc., 


. 

v>    -= 


1.1 


Fig.  216,  below  the  I.L.  with  a  radius  =  i|"  and  divide  and 
figure  it  as  shown. 

Since  the  plane  is  parallel  to  V.P.  its  horizontal  projection 
will  be  a  straight  line  i*,  2*, etc. 

For  the  second  position  revolve  the  said  horizontal  projection 
through  the  required  angle  of  45°  to  the  position  ah  .  .  .  .  iift, 


184 


MECHANICAL  DRAWING 


Fig.  216,  and  through  each  division  in  i*  .  .  .  .  ah  draw  arcs 
cutting  a*  ....  i*  in  points  2h$h  ....  This  is  the  hori- 
zontal projection  of  the  plane  when  making  an  angle  of  45° 
with  the  V.P. 

The  elevation  is  found  by  dropping  perpendiculars  from  the 
points  in  the  horizontal  projections  a*  ...  ii*  to  intersect 
horizontal  lines  drawn  through  the  correspondingly  numbered 


FIG.  217. 


points  in  the  elvation  and  through  these  intersections  draw  the 
elevation  or  vertical  project  of  the  second  position. 

For  the  third  position  make  a  tracing  of  the  elevation  of  the 
second  position,  numbering  all  the  points  as  before,  and  place 
the  tracing  so  that  the  diameter  ff  makes  the  required  angle  of 
60°  with  the  I.L.  and  transfer  to  the  drawing-paper,  Fig.  217. 

FIG.  218.  Draw  the  projections  of  a  regular  hexagonal  prism, 
3"  high  and  having  an  inscribed  circle  of  4!"  diameter:  (i) 
When  its  axis  is  parallel  to  the  V.P.  (2)  Draw  the  true  form  of 
a  section  of  the  prism  when  cut  by  a  plane  passing  through  it  a 
an  angle  of  30°  with  its  base.  (3)  Draw  the  projection  of  a  sec- 
tion when  cut  by  a  plane  passing  through  XX,  Fig.  218,  perpen- 
dicular to  both  planes  of  projection. 

The  drawing  of  the  I.L.  may  now  be  omitted. 


APPENDIX  TO  THE  REQUIRED  COURSE 


185 


For  the  plan  of  the  first  part  of  this  problem  draw  a  circle  with 
a  radius  =  to  2-3^",  and  circumscribe  a  hexagon  about  it,  as  shown 
by  ah,  bh,  b",  etc.,  Fig.  218.  To  project  the  elevation,  draw  at  a 
convenient  distance  from  the  plan  a  horizontal  line  parallel  to 
ahdh,  and  3"  below  it  another  line  parallel  to  it.  From  the 


FIG.  218. 


FIG.  219. 


points  ahbhchdh,  drop  perpendiculars  cutting  these  parallel  lines 
in  the  points  abvcd\  thus  completing  the  elevation  of  the  prism. 
Second  condition:  Draw  the  edge  view  or  trace  of  the  cutting 
plane  iV>  making  an  angle  of  30°  with  the  base  of  the  prism, 
locating  the  lower  end  4'  \"  above  the  base;  parallel  to  iV, 
and  at  a  convenient  distance  from  it  draw  a  straight  line  i,  4; 
at  a  distance  of  2^"  on  each. side  of  i,  4  draw  lines  3,  2  and  5,  6 
parallel  to  i,  4,  and  through  the  points  i^^V  let  fall  perpen- 


186  MECHANICAL  DRAWING  . 

diculars  cutting  these  three  parallel  lines  in  the  points  i,  2,  3,  4, 
5,  6;  join  these  points  by  straight  lines  as  shown,  and  a  true 
drawing  of  the  section  of  the  prism  as  required  will  result. 

For  the  third  condition  of  the  problem : 

Let  XX  be  the  edge  view  of  the  cutting  plane  and  conceive 
that  part  of  the  prism  to  the  right  of  XX  to  be  removed.  From 
the  horizontal  projection  of  the  prism  draw  a  right-hand  eleva- 
tion or  profile  projection,  and  through  the  points  XX  draw  the 
lines  enclosing  the  section,  and  hatch-line  it  as  shown. 

FIG.  219.  To  draw  the  development  of  the  lower  part  of  the 
prism  in  the  elevation  of  the  last  problem. 

To  the  right  of  the  elvation  in  Fig.  218,  prolong  the  base  line 
indefinitely  and  lay  off  upon  it  the  distances  ab,  be,  cd,  etc., 
Fig.  216,  each  equal  in  length  to  a  side  of  the  hexagon.  At  these 
points  erect  perpendiculars,  and  through  the  points  iV 3*4' 
draw  horizontal  lines  intersecting  the  perpendiculars  in  4,  3,  2,  i, 
etc.  At  be  draw  the  hexagon  aW,  cV,  dh  of  the  last  problem 
for  the  base,  and  at  i,  2  draw  the  section  i,  2,  3, 4,  5,  6  for  the  top. 

FIG.  220.  To  draw  the  projections  of  a  right  cylinder  3' 
diameter  and  3"  long,  (i)  When  its  axis  is  perpendicular  to 
the  H.P.  (2)  Draw  the  true  form  of  a  section  of  the  cylinder, 
when  cut  by  a  plane  perpendicular  to  the  V.P.,  making  an  angle 
of  30°  with  the  H.P.  (3)  Draw  the  development  of  the  upper 
part  of  the  cylinder. 

For  the  plan  of  the  first  condition,  describe  the  circle  i',  2', 
etc.,  with  radius  =  i  J"  and  from  it  project  the  elevation,  which 
will  be  a  square  of  3"  sides. 

For  the  second  condition :  Let  i ,  7  be  the  trace  of  the  cutting 
plane,  making  the  point  7,  %'  from  the  top  of  the  cylinder. 
Divide  the  circle  into  12  equal  parts  and  let  fall  perpendiculars 
through  these  divisions  to  the  line  of  section,  cutting  it  in  the 
points  i,  2,  3,  4,  etc.  Parallel  to  the  line  of  Section  i,  7  draw 
i "7"  at  a  convenient  distance  from  it,  and  through  the  points 
i,  2,  3,  4,  etc.,  draw  perpendiculars  to  i,  7,  intersecting  and 
extending  beyond  i"f.  Lay  off  on  these  perpendiculars  the 
distances  6"8"  =  6'8',  and  sV'^sV,  etc.,  and  through  the 
points  2",  3",  4",  etc.,  describe  the  ellipse. 


APPENDIX  TO  THE  REQUIRED  COURSE 


187 


For  the  development:  In  line  with  the  top  of  the  elevation 
draw  the  line  g'g"  equal  in  length  to  the  circumference  of  the 
circle,  and  divide  it  into  12  equal  parts  a',  b' ',  etc.,  a! ,  b",  etc. 
Through  these  points  drop  perpendiculars  and  through  the  points 
i,  2,  3,  etc.,  draw  horizontals  intersecting  the  perpendiculars  in 
the  points  i,  2,  3,  etc.,  and  through  these  points  draw  a  curve. 


FIG.  220. 


Tangent  to  any  point  on  the  straight  line  draw  a  3"  circle 
for  the  top  of  the  cylinder  and  tangent  to  any  suitable  point  on 
the  curve  transfer  a  tracing  of  the  ellipse. 

FIG.  221.  Draw  the  projections  of  a  right  cone  7"  high, 
with  a  base  6"  in  diam.,  pierced  by  a  right  cylinder  2"  in  diam- 
eter and  5"  long,  their  axes  intersecting  at  right  angles  3"  above 
the  base  of  the  cone  and  parallel  to  V.P.  Draw  first  the  plan  of 
the  cone  with  a  radius  =  3". 

At  a  convenient  distance  below  the  plan  draw  the  elevation 
to  the  dimensions  required. 

3"  above  the  base  of  the  cone  draw  the  center  line  of  the 
cylinder  CD,  and  about  it  construct  the  elevation  of  the  cylinder, 
which  wiJl  appear  as  a  rectangle  2"  wide  and  2^"  each  side  of  the 
axis  of  the  cone.  The  half  only  appears  in  the  figure. 

To  project  the  curves  of  itersection  between  the  cylinder 


188 


MECHANICAL  DRAWING 


and  cone  in  the  plan  and  elevation:  Draw  to  the  right  of  the  cyl- 
inder on  the  same  center  line  a  semicircle  with  a  radius  equal  that 
of  the  cylinder.  Divide  the  semicircle  into  any  number  of  parts, 
as  i,  2,  3,  4,  etc.  Through  i,  i  draw  the  perpendiculars  A"  i" 
equal  in  length  to  the  height  of  the  cone,  and  through  A"  draw 
the  line  4  "4"  tangent  to  the  semicircle  at  the  point  4,  and 


FIG.  221. 


FIG.  222. 


through  the  other  divisions  of  the  semicircle  draw  lines  from  A" 
to  the  line  i'V'?  meeting  it  in  the  points  3/V/. 

From  all  points  on  the  line  I'V'?  viz.,  I'YYV,  erect  per- 
pendiculars to  the  center  line  of  the  plan,  cutting  it  in  the  points 
ii'Wsi'V,  and  with  ii"  as  the  center  draw  the  arcs  2i"-2, 
31"  —  3,  41"— 4  above  the  center  line  of  the  plan,  and  through  the 
points  2,  3,  4  draw  horizontals  to  intersect  the  circle  of  the  plan 
in  the  points  2  '3  V>  and  lay  off  the  same  distances  on  the  other 


APPENDIX  TO  THE  REQUIRED  COURSE  189 

side  of  the  center  line  of  the  plan  in  same  order,  viz.,  2 '3 '4'. 
Through  each  of  these  points  on  the  circumference  of  the  circle 
of  the  plan  draw  radii  to  its  center  A' ,  and  through  the  same 
points  also  in  the  plan  let  fall  perpendiculars  to  the  base  of  the 
elevation  of  the  cone,  cutting  it  in  the  points  2 '3  V;  and  from  the 
apex  A  of  the  elevation  of  the  cone  draw  lines  to  the  points  2  '3  V 
on  the  base.  Horizontal  lines  drawn  through  the  points  of 
division  2,  3,  4  on  the  semicircle  will  intersect  the  elements  A-2\ 
A-$',  A-A!  of  the  cone  in  the  points  2/3/4/;  these  will  be  points  in 
the  elevation  of  the  curve  of  intersection  between  the  cylinder 
and  the  cone. 

The  plan  of  the  curve  is  found  by  erecting  perpendiculars 
through  the  points  in  the  elevation  of  the  curve  to  intersect  the 
radial  lines  of  the  plan  in  correspondingly  figured  points,  through 
which  trace  the  curve  as  shown.  Repeat  for  the  other  half  of  the 
curve. 

FIG.  222.  To  draw  the  development  of  the  half  cone,  show- 
ing the  hole  penetrated  by  the  cylinder. 

With  center  41",  Fig.  222,  and  element  Ai'  of  the  cone, 
Fig.  128,  as  radius,  describe  an  arc  equal  in  length  to  the.  semi- 
circle of  the  base  of  the  cone.  Bisect  it  in  the  line  4i"i,  and 
on  each  side  of  the  point  i  lay  off  the  distances  2,  3,  4,  equal 
to  the  divisions  of  the  arc  in  the  plan  Fig.  128,  and  from  these 
points  draw  lines  to  4",  the  center  of  the  arc.  Then  with  radii 
A  -a,  b,  c,  d,  e,  respectively,  on  the  elevation  Fig.  128,  and  center 
41"  draw  arcs  intersecting  the  lines  drawn  from  the  arc  XX  to 
its  center  41".  Through  the  points  of  intersection  draw  the 
curve  as  shown  by  Fig.  222. 

FIG.  223.  To  draw  the  development  of  the  half  of  a  trun- 
cated cone,  given  the  plan  and  elevation  of  the  cone. 

Divide  the  semicircle  of  the  plan  into  any  number  of  parts, 
then  with  A  as  center  and  Ai  as  radius,  draw  an  arc  and  Jay 
off  upon  it  from  the  point  i  the  divisions  of  the  semicircle  from 
i  to  9,  draw  gA.  Then  with  center  A  and  radius  AB  draw  the 
arc  BC.  iBCg  is  the  development  of  the  half  of  the  cone  approx- 
imately. 

FIG.  224.     To   draw    the   curve   of  intersection   of  a   small 


190 


MECHANICAL  DRAWING 


cylinder  with  a  larger.  To  the  left  of  the  center-line  of  Fig. 
224  is  a  half  cross-section,  and  to  the  right  a  half  elevation 
of  the  two  cylinders. 

Draw  the  half  plan  of  the  small  cylinder,  which  will  be  a 
semicircle,  and  divide  it  into  any  convenient  number  of  parts, 
say  12. 

From  each  of  these  divisions  drop  perpendiculars. 


On  the  half  cross-section  these  perpendiculars  intersect 
the  circumference  of  the  large  cylinder  in  the  points  i',  2',  etc. 
Through  these  points  draw  horizontals  to  intersect  in  corre- 
sponding points  the  perpendiculars  on  the  half  elevation. 
Through  the  latter  points  draw  the  curve  of  intersection  C. 

To  draw  the  development  of  the  smaller  cylinder  of  the  last 
problem. 

Draw  a  rectangle,  Fig.   225,  with  sides  equal  to  the  cir- 


APPENDIX  TO  THE  REQUIRED  COURSE 


191 


cumference  and  length  of  the  cylinder,  respectively,  and  divide 
it  into  24  equal  parts. 

Make  AB" ',  i  i',  3  3',  etc.,  Fig.  225,  equal  to  AB,  iV, 
2V,  3 '3")  etc.,  Fig.  224,  and  draw  the  developed  curve  of 
intersection 

To  draw  the  orthographic  projections  of  a  cylindrical  dome 
riveted  to  a  cylindrical  boiler  of  given  dimensions. 

Let  the  dimensions  of  the  dome  and  boiler  be:  dome 
26  J"  diameter  X  2 7"  high,  boiler  54"  diameter,  plates  \"  thick. 

Apply  to  the  solution  of  this  problem  the  principles  ex- 
plained for  Fig.  224. 


FIG.  227. 


FIG.  226 


FIG.  225. 

When  your  drawings  are  completed,  compare  them  with 
Figs.  226  and  227,  which  are  the  projections  required  in  the 
problem. 

Letter  or  number  the  drawing  and  be  prepared  to  explain 
how  the  different  projections  were  found. 

To  draw  the  development  of  the  top  gusset-sheets  of  a  locomo- 
tive wagon-top  boiler  of  given  dimensions. 

First  draw  the  longitudinal  cross-section  of  the  boiler  to 
dimensions  given  by  Fig.  228,  using  the  scale  of  i"  =  i  ft. 

Then    at    any    convenient   point    on   your   paper    draw    a 


192 


MECHANICAL  DRAWING 


straight  line,  and  upon  it  lay  off  a  distance  AB  35^"  long  = 
the  straight  part  of  the  top  of  the  gusset-sheet  G,  Fig.  225-228. 
With  center  A  and  a  radius  =  2  7!"  (the  largest  radius  of  the 


gusset) +6"  (the  distance  from  the  center  of  the  boiler  to  the 
center  of  the  gusset  C,  Fig.  228)  =33!",  draw  arc  i. 

With  center  B  and  a  radius  =  26|  (the  smallest  radius    of 


APPENDIX  TO  THE  REQUIRED  COURSE  193 

the  gusset)  draw  arc  2.  Tangent  to  these  arcs  draw  the 
straight  line  i,  2  extended,  and  through  the  points  A  and 
draw  lines  i,  A  and  2,  B  perpendicular  to  i,  2. 

Take  a  point  on  the  perpendicular  i,  2,  6"  from  the  point 
i  as  a  center  and  through  the  point  A  draw  an  arc  with  a 
radius  =  27"!. 

With  point  2  as  a  center  and  2B  as  a  radius  (26f")  draw 
an  arc  through  B  to  meet  the  line  i,  2. 

Divide  both  arcs  into  any  number  of  parts,  say  12,  and 
through  these  divisions  draw  lines  perpendicular  to  and  inter- 
secting i  A  and  2J3,  respectively.  Through  these  intersections 
draw  indefinite  horizontals  and  on  these  horizontals  step  off 
the  length  of  the  arcs,  with  a  distance  =  one  of  the  12  divisions 
as  follows: 

On  the  first  horizontals  lay  off  the  length  of  the  arc  Ai' 
and  Bi'  =  Ai  and  Bi  respectively.  Then  from  i'  lay  off 
the  same  distance  to  2'  on  the  second  horizontals,  etc. 
Through  these  points  draw  curves  Ai$'  and  Bi2f.  Join 
points  12'  and  13'  with  a  straight  line.  Then  ABi2,  13  will 
be  the  developed  half  of  the  straight  part  of  the  gusset.  , 

On  the  two  ends  or  front  and  back  of  the  gusset  we  have 
now  to  add  i"  for  clearance+3f"  for  lap-f i"  allowance  for 
truing  up  the  plates,  total  =  5!".  And  to  the  sides  2§"  for 
lap+^"  allowance  for  truing  up,  total  =  3!". 

The  outline  of  the  developed  sheet  may  now  be  drawn  to 
include  these  dimensions  with  as  little  waste  as  possible,  as 
shown  by  Fig.  229.  Extreme  accuracy  is  necessary  in  making 
this  drawing,  as  the  final  dimensions  must  be  found  by 
measurement. 

To  draw  the  projections  of  a  V-threaded  screw  and  its  nut 
of  3"  diameter  and  f  "  pitch. 

Begin  by  drawing  the  center  line  C,  Fig.  230,  and  lay  off 
on  each  side  of  it  the  radius  of  the  screw  \\n '.  Draw  AB 
and  6D.  Draw  A6  the  bottom  of  the  screw,  and  en  AB  step 
off  the  pitch  =  f",  beginning  at  the  point  A. 

On  line  6D  from  the  point  6  lay  off  a  distance  =  half  the 
pitch  =  f ',  because  when  the  point  of  the  thread  has  com- 


194 


MECHANICAL  DRAWING 


pleted  half  a  revolution  it  will  have  risen  perpendicularly  a 
distance  =  half  the  pitch,  viz.,  f". 

Then  from  the  point  6"  on  6D  step  off  as  many  pitches 
as  may  be  desired.  From  the  points  of  the  threads  just 
found,  draw  the  30°  triangle  and  T-square  the  V  of  the 


FIG.  230. 


FIG.  231. 


threads  intersecting  at  the  points  b.  .b. .    the  bottom  of  the 
threads. 

At  the  point  O  on  line  A6  draw  two  semicircles  with 
radii  =  the  top  and  bottom  of  the  thread,  respectively.  Divide 
these  into  any  number  of  equal  parts  and  also  the  pitch  P 
into  the  same  number  of  equal  parts.  Through  these  divisions 
draw  horizontals  and  perpendiculars  intersecting  each  other 
in  the  points  as  shown  by  Fig.  230,  which  shows  an  elevation 
partly  in  section  and  a  section  of  a  nut  to  fit  the  screw. 


APPENDIX  TO  THE  REQUIRED  COURSE 


195 


Through  the  points  of  intersection  draw  the  curves  of  the 
helices  shown,  using  Irregular  Curve,  No.  13,  Fig.  28. 

FIG.  231.  To  draw  the  projection  of  a  square-threaded  screw 
3"  diameter  and  i"  pitch  and  also  a  section  of  its  nut. 

The  method  of  construction  is  the  same  as  for  the  last 
problem,  and  is  illustrated  by  Fig.  231. 


FIG.  232. 

FIG.  232.  To  draw  the  projections  of  a  square  double- 
threaded  screw  of  3"  diameter  and  2"  pitch,  and  also  a  section  of 
its  nut. 

Proceed  in  the  same  manner  as  explained  for  the  V- 
threaded  screw,  Fig.  230. 

FIG.  233.  To  draw  the  curve  of  intersection  that  is  formed  by 
a  plane  cutting  an  irregular  surface  of  revolution. 

i st.  Draw  the  complete  outline  of  the  connecting  rod  end 
partly  shown  in  Fig.  233.  Complete  all  three  views. 


196 


MECHANICAL  DRAWING 


2d.  Divide  line  AB  into  any  number  of  parts,  say  14, 
preferably  equal  parts. 

3d.  With  center  D  and  radii  equal  to  the  distances  from 
D  to  the  several  divisions  on  AB  already  determined,  revolve 
those  points  to  cut  the  line  CD  in  a  corresponding  number  of 
points. 

4th.  From  the  points  on  CD  draw  horizontals  in  narrow 
lines  to  the  left  of  CD,  cutting  points  in  the  if"  radial  curve  G. 

5th.  From  all  these  points  in  G  drop  perpendiculars  to 
intersect  horizontals  from  all  the  points  in  AB.  Through  the 


FIG.  233. 

points  of  intersection  draw  the  required  curve  of  intersec- 
tion I. 

To  find  the  curve  in  the  plan  at  E. 

i st.  Divide  the  line  AC  into  a  convenient  number  of  equal 
or  unequal  parts  and  revolve  into  CD. 

2d.  Through  these  points  at  C  draw  horizontals  to  inter- 
sect curve  G  extended  and  through  points  thus  found  erect 
perpendiculars. 

3d.  With  the  dividers  take  the  several  distances  from 
CD  along  the  line  CA  and  lay  them  off  from  E  to  cut  the 
corresponding  perpendiculars  from  the  extended  part  of  the 
curve  G.  Draw  the  required  curve  through  the  points  of 
intersection. 


APPENDIX  TO  THE  REQUIRED  COURSE 


197 


Figs.  233,  234,  and  235  show  examples  of  engine  connect- 
ing  rod   ends   where    the    curve   /   is   formed   by   the   inter- 


FIG.  234. 

section  of  the  flat  stub  end  with  the  surface  of  revolution  of 
the  turned  part  of  the  rod. 

I 


FIG.  235. 

The  description  of  the  method  used  for  finding  the  curve 
of  intersection  /  in  Fig.  233  by  intersecting  planes  will  apply 
equally  as  well  to  Figs.  234  and  235. 


198  MECHANICAL  DRAWING 

SHADE  LINES,  SHADES  AND  SHADOWS 

Shade  lines  were  used  quite  generally  some  years  ago  on 
commercial  drawings.  They  improved  the  appearance  of  the 
drawing  but  the  cost  of  applying  them  outweighed  their 
value  and  so  were  abandoned  except  for  special  drawings. 

The  simple  methods  of  application  are  included  here  for 
the  benefit  of  those  who  nay  desire  to  use  them. 

The  Shading  of  the  curved  surfaces  of  machine  parts  is 
sometimes  practiced  on  specially  finished  drawings,  but  on 
working  drawings  most  employers  will  not  allow  shading 
because  it  takes  too  much  time,  and  is  not  essential  to  a  quick 
and  correct  reading  of  a  drawing,  especially  if  a  system  of 
shade  lines  is  used. 

Some  of  the  principles  Of  shade  lines  and  shading  are 
given  below,  with  a  few  problems  illustrating  their  commonest 
applications. 

The  shadows  which  opaque  objects  cast  on  the  planes  of 
projection  or  on  other  objects  are  seldom  or  never  shown  on 
a  working  drawing,  but  are  often  projected  on  architecture 
and  special  drawings. 

••{ 

CONVENTIONS 

The  Source  of  Light  is  considered  to  be  at  an  infinite  dis- 
tance from  the  object,  therefore  the  Rays  of  Light  will  be  rep- 
resented by  parallel  lines. 

The  Source  of  Light  is  considered  to  be  fixed,  and  the 
Point  of  Sight  situated  in  front  of  the  object  and  at  an  infinite 
distance  from  it,  so  that  the  Visual  Rays  are  parallel  to  one 
another  and  perpendicular  to  the  plane  of  projection. 

Shade  Lines  divide  illuminated  surfaces  from  dark  surr 
faces. 

Dark  surfaces  are  not  necessarily  to  be  defined  by  those 
surfaces  which  are  darkened  by  the  shadow  cast  by  another 
-part  of  the  object,  but  by  reason  of  their  location  in  relation 
to  the  rays  of  light. 


APPENDIX  TO  THE  REQUIRED  COURSE 


199 


It  is  the  general  practice  to  shade-line  the  different  pro- 
jections of  an  object  as  if  each  projection  was  in  the  same 
plane,  e.g.,  suppose  a  cube,  Fig.  236,  situated  in  space  in  the 
third  angle,  the  point  of  sight  in  front  of  it,  and  the  direction 
of  the  rays  of  light  coinciding  with  the  diagonal  of  the  cube, 
as  shown  by  Fig.  237.  Then  the  edges  avbv,  Vcv  will  be 
shade  lines,  because  they  are  the  edges  which  separate  the 
illuminated  faces  (the  faces  upon  which  fall  the  rays  of  light) 
from  the  shaded  faces,  as  shown  by  Fig.  237. 


\ 


FIG.  236. 


FIG.  237. 


Now  the  source  of  light  being  fixed,,  let  the  point  of  sight 
remain  in  the  same  position,  and  conceive  the  object  to  be 
revolved  through  the  angle  of  90°  about  a  horizontal  axis  so 
that  a  plan  of  the  top  of  the  object  is  shown  above  the  ele- 
vation, and  as  the  projected  rays  of  light  falling  in  the  direc- 
tion of  the  diagonal  of  a  cube  make  angles  of  45°  with  the 
horizontal,  then  with  the  use  of  the  45°  triangle  we  can  easily 
determine  that  the  lower  and  right-hand  edges  of  the  plan 
as  well  as  of  the  elevation  should  be  shade  lines. 

This  practice  then  will  be  followed  in  this  work,  viz.: 
Shade  lines  shall  be  applied  to  all  projections  of  an  object, 
considering  the  rays  of  light  to  fall  upon  each  of  them  from 
the  same  direction. 


200  MECHANICAL  DRAWING 

Shade  lines  should  have  a  width  equal  to  3  times  that  of 
the  other  outlines.  •  Broken  lines  should  never  be  shade  lines. 

The  outlines  of  surfaces  of  revolution  should  not  be  shade 
lines.  The  shade-lined  figures  which  follow  will  assist  in 
illustrating  the  above  principles;  they  should  be  studied  until 
understood. 

SHADES 

The  shade  of  an  object  is  that  part  of  the  surface  from 
which  light  is  excluded  by  the  object. 

The  line  of  shade  is  the  line  separating  the  shaded  from 
the  illuminated  part  of  an  object,  and  is  found  where  the  rays 
of  light  are  tangent  to  the  object. 

Brilliant  Points.  "  When  a  ray  of  light  falls  upon  a  sur- 
face which  turns  it  from  its  course  and  gives  it  another  direc- 
tion, the  ray  is  said  to  be  reflected.  The  ray  as  it  falls  upon 
the  surface  is  called  the  incident  ray,  and  after  it  leaves  the 
surface  the  reflected  ray.  The  point  at  which  the  reflection 
takes  place  is  called  the  point  of  incidence. 

"It  is  ascertained  by  experiment — 

"  (a)  That  the  plane  of  the  incident  and  reflected  rays  is 
always  normal  to  the  surface  at  the  point  of  incidence; 

"  (b)  That  at  the  point  of  incidence  the  incident  and 
reflected  rays  make  equal  angles  with  the  tangent  plane  or 
normal  line  to  the  surface. 

"  If  therefore  we  suppose  a  single  luminous  point  and  the 
light  emanating  from  it  to  fall  upon  any  surface  and  to  be 
reflected  to  the  eye,  the  point  at  which  the  reflection  takes 
place  is  called  the  brilliant  point.  The  brilliant  point  of  a 
surface  is,  then,  the  point  at  which  a  ray  of  light  and  a  line 
drawn  to  the  eye  make  equal  angles  with  the  tangent  plane 
or  normal  line — the  plane  of  the  two  lines  being  normal  to 
the  surface." — Davies:  Shades  and  Shadows. 

Considering  the  rays  of  light  to  be  parallel  and  the  point 
of  sight  at  an  infinite  distance,  the  brilliant  point  on  the  sur- 
face of  a  sphere  is  found  as  follows:  Let  ACCV  and  A*Ch, 


APPENDIX  TO  THE  REQUIRED  COURSE 


201 


Fig.  238,  be  a  ray  of  light  and  A'Ah  a  visual  ray.  Bisect 
the  angles  contained  between  the  ray  of  light  and  the  visual 
ray  as  follows:  Revolve  AVCV  about  the  axis  A°  until  it 
becomes  parallel  to  the  horizontal  plane  at  AVC\.  At  C\ 
erect  a  perpendicular  to  intersect  a  horizontal  through  Ch 
at  Cih  join  CiflLh  (L  may  be  any  convenient  point  on  the  line 
of  vision),  bisect  the  angle  LhAhC*  with  the  line  A*!)". 
Join  CnLh  and  through  the  point  Dh,  draw  a  horizontal 


FIG.  238. 

cutting  ChLh  at  Dih  then  A^D^  is  the  horizontal  projection 
of   the  bisecting  line.     A  plane  drawn  perpendicular   to   this 
bisecting  line  and  tangent  to  the  sphere  touches  the  surface 
at  the  points  B'Bih  where  the  bisecting  lines  pierce  it.     There- 
fore BvBh  are  the  two  projections  of  the  brilliant  point. 
The  point  of  shade  can  be  found  as  follows: 
Draw  AhG,  Fig.  238,  making  an  angle  of  45°  with  a  hori- 
zontal.    Join   the  points  E   and   F  with  a  straight  line  EF. 
Lay  off  on  AhG    a    distance    equal    to    EF,    and    join    EG, 


202  MECHANICAL  DRAWING 

Parallel  to  EG  draw  a  tangent  to  the  sphere  at  the  point  T. 
Through  T  draw  TPh  perpendicular  to  AhG.  From  the  point 
P*  drop  a  perpendicular  P\  Pv  is  the  point  of  shade. 

FIG.  239.  To  shade  the  elevation  of  a  sphere  with  graded 
arcs  of  circles. 

First  find  the  brilliant  point  and  the  point  of  shade,  and 
divide  the  radius  i,  2,  into  a  suitable  number  of  equal  parts, 
and  draw  arcs  of  circles  as  shown  by  Fig.  239,  grading  them 
by  moving  the  center  a  short  distance  on  each  side  of  the 
center  of  the  sphere  on  the  line  B*2  and  varying  the  length 
of  the  radii  to  obtain  a  grade  of  line  that  will  give  a  proper 
shade  to  the  sphere.  It  is  desirable  to  use  a  horn  center  to 
protect  the  center  of  the  figure. 


FIG.  239.  FIG.  240. 

FIG.  240  sliows  tlie  stippling  method  of  shading  the  sphere. 

FIG.  241.     To  shade  a  right  cylinder  with  graded  right  lines. 

Find  the  line  of  light  B9  by  the  same  method  used  to  find 
the  brilliant  point  on  the  sphere,  except  that  the  line  of  light 
is  projected  from  the  point  Bh  where  the  bisection  line  AhD 
cuts  the  circle  of  the  cylinder. 

The  line  of  shade  is  found  where  a  plane  of  rays  is  tan- 
gent to  the  cylinder  at  5"  and  5*. 

FIG.  242  sliows  how  the  shading  lines  are  graded  from  the 
line  of  shade  to  the  line  of  light. 

It  will  be  noticed  that  the  lines  grow  a  little  narrower  to 
the  right  of  the  line  of  shade  on  Fig.  242;  this  shows  where 


APPENDIX  TO  THE  REQUIRED  COURSE 


203 


the  reflection  of  the  rays  of  light  partly  illumine  the  outline 
of  the  cylinder. 

FIG.  243.  To  shade  the  concave  surface  of  a  section  of  a 
hollow  cylinder. 

Find  the  element  of  light  and  grade  the  shading  lines  from 
it  to  both  edges  as  shown  by  Fig.  243. 


FIG.  241. 


FIG.  242, 


FIG.  243. 


PIG.  244. 


FIG.  244  shows  a  conventional  method  of  shading  a  hexagonal 
nut. 

FIG.  245.  To  shade  a  right  cone  with  graded  right  lines 
tapering  toward  the  apex  of  the  cone. 

Find  the  elements  of  light  and  shade  as  shown  by  Fig.  245, 
and  draw  the  shading-lines  as  shown  by  Fig.  246,  grading 


204 


MECHANICAL  DRAWING 


their  width  toward  the  light  and  tapering  them  toward  the 
apex  of  the  cone. 

The  mixed  appearance  of  the  lines  near  the  apex  of  the 
cone  on  Fig.  246  can  usually  be  avoided  by  letting  each  line 
dry  before  drawing  another  through  it,  or  as  some  draftsmen 
do,  stop  the  lines  just  before  they  touch./ 


FIG.  246.' 


SHADOWS 

/  Let  R,  Fig.  247,  be  the  direction  of  the  rays  of  light 
and  C  an  opaque  body  between  the  source  of  light  and  a 
surface  S.  The  body  C  will  prevent  the  rays  from  passing 
in  that  direction,  and  its  outline  will  be  projected  at  D  on 
the  surface  S.  D  is  the  shadow  of  C. 

The  line  which  divides  the  illuminated  portion  of  the 
surface  S  from  the  shadow  D  is  called  the  line  of  shadow. 

Shadow  of  a  Point.  If  a  line  is  drawn  through  a  point  in 
space  in  a  direction  opposite  to  the  source  of  light,  the  point 
in  which  this  line  pierces  the  plane  of  projection  is  the  shadow 
of  the  point  on  that  plane. 

To  find  the  shadow  on  the  H.P.  of  a  point  in  space  in 
the  first  dihedral  angle- 


APPENDIX  TO  THE  REQUIRED  COURSE 


205 


Let  A,  Fig.  248,  be  the  point  in  space,  and  R  the  direction 
of  the  ray  of  light;  then  A\H  is  the  shadow  of  the  point 
A  on  H.P.  and  AHAiH  is  the  horizontal  projection  and  AVA\V 


D 


FIG.  247. 


FIG.  248. 

the  vertical  projection  of  R.  Bv  is  the  point  where  R  pierces 
V  when  prolonged  below  H.P.,  and  BH  is  its  horizontal  pro- 
jection in  the  G.L.  The  projections  of  R  would  then  be 
AVBV. 


206 


MECHANICAL  DRAWING 


The  shadow  of  a  point  in  V  may  be  found  in  a  similar 
manner. 

Shadows  of  Right  Lines.  The  shadow  of  a  right  line  on 
a  plane  may  be  determined  by  finding  the  shadows  of  two  of 
its  points  and  joining  these  by  a  right  line;  e.g.,  the  shadow 
of  the  line  AB,  Fig.  249,  on  H.P.  is  found  as  follows: 

Through  the  points  AVBV  draw  the  rays  Av AIV  and  BvBiv 
to  intersect  the  plane  of  projection  in  G.L.  in  the  points  A\v 
and  Biv;  from  these  points  drop  perpendiculars  to  meet  rays 
drawn  through  AH  and  BH  in  the  points  A\H  and  B\H.  A  line 
drawn  from  A\H  to  B\R  is  the  shadow  of  AB  on  H.P 


If  a  right  line  is  parallel  to  the  plane  of  projection  its  shadow 
will  be  parallel  to  the  line  itself. 

If  a  line  coincides  with  a  ray  of  light,  its  shadow  on    any 
surface  will  be  a  point. 

To  find  the  shadow  of  a  right  line  on  V.P.  and  H.P.: 
Let  AB,  Fig.  250  be  the  given  line.  Find  the  shadows 
points  A  and  B  by  passing  rays  through  each  of  their  projections 
to  make  angles  of  45°  with  G.L.  The  shadow  of  AH  on  H.P .  is 
found  at  A  IH,  and  that  of  BH  at  B\H,  where  the  rays  through  these 
points  intersect  the  H.P.  The  shadow  of  A v  on  V.P.  is  found 


APPENDIX  TO  THE  REQUIRED  COURSE 


207 


at  Aiv  and  that  of  Bv  at  Biv,  where  the  rays  through  these 
points  intersect  V.P.  Join  A\H  and  B\H  with  a  straight  line 
and  we  have  the  shadow  of  AB  on  H.P.,  and  the  shadow  on  V.P. 
is  found  in  the  same  way  by  joining  with  a  straight  line  the  points 
,4/and.B/. 

That  part  of  the  shadow  which  falls  on  V.P.  below  G.L., 
and  on  H.P.  above  G.L.,  is  called  the  secondary  shadow,  because 
it  makes  a  second  intersection,  i.e.,  it  is  conceived  to  have  passed 
through  V.P.  and  made  an  intersection  with  H.P.  behind  V.P. 


FIG.  250. 


With  the  use  of  the  secondary  shadow  problems  like  this  are 
easier  of  solution. 

A  BCD,  Fig.  251,  is  a  square  plate  parallel  to  V.P.;  find  its 
shadow  on  H.P. 

Through  the  points  Av,  Bv,  Dv,  and  AHCH,  BHDH,  draw  rays 
making  the  angle  of  45°  (or  any  other  angle  which  may  be 
adopted)  with  G.L.,  and  determine  the  shadows  of  these  points 
as  explained  in  Fig.  248.  They  will  be  found  in  the  points 
AiHBiH,  CIH,  DIH.  Join  these  points  with  right  lines  and  they 
will  form  the  line  of  shadow  of  the  square  plate  on  H.P. 

FIG.  252.  To  find  the  shadow  of  a  cube  on  V.P.  with  one  face 
in  V.P.  and  the  other  faces  parallel  or  perpendicular  to  H.P. 


208 


MECHANICAL  DRAWING 


FIG.  251. 


DrB 


FIG.  252. 


APPENDIX  TO  THE  REQUIRED  COURSE 


209 


FIG.  252  shows  the  cube  in  the  given  position.  The  line  of  shade 
is  composed  of  edges  EF,  FG,  GD,  DB,  and  the  edges  AE  and  AB  in 
V.P.  which  coincide  with  their  shadows. 

The  shadow  of  EF  is  EvFi,  of  FG  is  Fid,  of  GD 
is  GiDi,  of  DB  is  DiBv.  The  shadows  of  the  edges  AE 
and  AB  coincide  with  the  lines.  These  shadows  are  found 
by  the  same  rules  used  for  finding  the  shadows  of  a  line 
in  Fig.  250.  The  line  of  shadow  is  BvD1GiF1FvEvAvDv. 
The  visible  line  of  shadow  is  BvDiGiF1EvCvDv. 

FIG.  253.  To  find  the  shadow  of  a  rectangular  abacus  on  the 
face  of  a  rectangular  pillar. 


FIG.  253. 


Assume  the  norizontal  and  vertical  projections  of  the  abacus 
and  pillar  to  be  as  shown  in  Fig.  253. 

The  line  of  shade  of  the  abacus  is  seen  to  be  the  edges  A  \HBiB 
and  AiHCiH.  The  plane  of  rays  through  edge  AiHBiH  is  perpen- 
dicular to  V.P.  and  the  line  A\VEV  is  its  vertical  projection  or 
trace;  its  horizontal  trace  is  A  \HEH.  The  shadow  on  the  left  side 
face  is  vertically  projected  in  the  point  E\v  where  the  plane  of 
rays  intersects  that  face.  The  ray  through  the  point  A\H  pierces 
the  front  face  in  the  point  EH,  which  is  the  shadow  of  AIH, 
and  EiHEa,  Elvev  is  the  shadow  of  the  part  FHAiH  on  this  face. 


210 


MECHANICAL  DRAWING 


The  line  A\HC\H  is  parallel  to  the  front  face,  therefore  its 
shadow  on  it  will  be  parallel  to  itself  and  pass  through  E. 

The  visible  line  of  shadow  is  now  found  to  be  iEivEvEv  2  i. 

FIG.  254.  Construct  the  shade  of  an  upright  hexagonal  prism 
and  its  shadow  on  both  planes. 

FIG.  254  shows  the   given   prism  with   its   line   of   shade 


FIG.  254. 


AivBlvEivDvFv  on  the  vertical  projection,  CHDHFHEH  on  the 
horizontal  projection,  and  its  shadow  on  both  planes. 

FIG.  255.  Given  a  circular  plate  parallel  to  one  coordinate 
plane:  construct  its  shadow  on  the  other  plane. 

Let  AVBVCVDV  and  AHCH,  Fig.  255,  be  the  projections  of 
the  circular  plate. 

Circumscribe  a  square  EVGV  about  the  circle;  its  shadow  on 
H.P.  will  be  the  parallelogram  AHGH,  and  the  shadows  of  the 
points  AVBVCVDV  are  projected  in  the  points  AiHBiHCiHDiH. 


APPENDIX  TO  THE  REQUIRED  COURSE 


211 


The  shadow  of  the  inscribed  circle  is  an  ellipse  tangent  to  the 
parallelogram  at  the  points  AiHBiHCiHDiH,  with  BiHDiH  and 
Ai"CiH  as  conjugate  diameters. 

The  position  and  length  of  the  axes  of  the  ellipse  of  shadow 
may  be  found  as  follows: 

Erect  a  perpendicular  at  the  point  CF,  making  GVKV  equal 
to  radius  of  the  circle  draw  KOP\  then  KP  is  equal  to  the  major 
and  MK  to  the  minor  axis,  and  angle  0  is  twice  the  angle  of  the 
transverse  axis  with  the  horizontal  conjugate  diameter;  i.e., 
KP  is  equal  to  i,  2,  MK  to  3,  4,  and  2,  OiCA  or  angle  8, 
is  equal  to  half  KOC\ 


FIG.  255. 


IG.  256.  Find  the  shade  of  a  cylindrical  column  and  abacus 
and  the  shadow  of  the  abacus  on  the  column. 

Let  AVBVCV  and  AHBHCH,  Fig.  256,  be  the  projections 
of  the  abacus,  DHEHF"  and  DHDVGVFH  the  projections  of  the 
column. 

The  line  of  shade  on  the  column  is  found  by  passing  two 
planes  of  rays  tangent  to  the  column  perpendicular  to  H.P. 
and  parallel  to  the  horizontal  projection  of  the  ray  of  light. 
KL  and  EH  are  the  traces  of  these  planes  tangent  to  the  column 


212 


MECHANICAL  DRAWING 


at  the  points  Z,,  and  EH  and  MN  the  visible  line  of  deepest  shade 
on  the  cylindrical  column. 

The  deepest  line  of  shade  i,  2  on  the  abacus  is  found  in  the 
same  way. 

The  line  of  shadow  on  the  column  of  that  portion  of  the  lower 
circumference  of  the  abacus  which  is  toward  the  source  of  light 
is  found  by  passing  vertical  planes  of  rays,  as  3,  4  to  determine 
any  number  of  points  in  the  line,  and  joining  these  points  by  a 
line  as  shown  in  Fig.  256. 


G-A 


FIG.  256. 

FIG.  257.  Find  the  shade  of  an  oblique  cone  and  its  shadow  on 
H.P 

Take  the  cone  as  given  in  Fig,  257  Pass  two  planes  of 
rays  tangent  to  the  cone;  tneir  elements  of  contact  will  be 
the  deepest  lines  of  shade.  To  determine  the  elements  of 
contact  draw  a  ray  through  CF;  C\H  is  its  hor.  trace.  From 
CIH  draw  lines  tangent  to  the  base  at  D  and  E\  the  lines  of 
contact  are  CE  and  CD,  and  ECD  is  the  line  of  shade. 

The  visible  line  of  shade  on  H.P.  is  EHDH,  and  on  V.P. 
CVEV.  The  shadow  on  H.P.  is  EHCiHDH. 

Conic  Sections.  Fig.  258  shows  a  right  circular  cone  cut 
by  planes  i,  2,  3,  and  4.  Plane  i,  perpendicular  to  the  axis, 


APPENDIX  TO  THE  REQUIRED  COURSE 


213 


cuts  a  circle.  Plane  2  cuts  the  cone  at  an  angle  greater  than 
that  of  the  elements,  and  the  section  is  an  ellipse.  Plane  3 
cuts  the  cone  at  an  angle  equal  to  that  of  the  elements  and 
gives  a  parabola.  Plane  4  cuts  the  cone  at  a  smaller  angle 
than  that  of  the  elements  and  the  section  is  hyperbola.  The 


figure  marked  A  is  the  elevation  of  the  cone  showing  the  cutting 
planes.  B  is  the  plane  of  the  cone  atnd  the  sections  cut  from 
it.  C  is  the  profile.  D  is  the  developments  or  true  sizes  of 
the  truncated  cone  below  planes  i,  2,  3,  and  4.  E  is  the  true 
section  of  the  hyperbola.  F  the  true  section  of  parabola,  and 
G  the  true  section  of  the  ellipse, 


PRESENT  PRACTICE  IN  DRAFTING  ROOM  CON- 
VENTIONS AND  METHODS  IN  MAKING  PRACTI- 
CAL WORKING  DRAWINGS. 


SUMMARY  REPORT  OF  AN  INVESTIGATION  MADE  BY  THE  WRITER 
WITH  THE  AUTHORITY  OF  THE  ARMOUR  INSTITUTE  OF 
TECHNOLOGY,  CHICAGO,  ILL.,  INTO  THE  PRESENT  PRAC- 
TICE OF  THE  LEADING  DRAFTSMEN  IN  THE  UNITED  STATES, 
IN  THE  USE  OF  STANDARD  CONVENTIONS  AND  METHODS 
WHEN  MAKING  COMMERCIAL  WORKING  DRAWINGS. 

A  circular  letter  accompanied  by  a  list  of  thirty-five  questions 
was  submitted  to  two  hundred  leading  firms  in  the  United  States, 
embracing  nearly  all  kinds  of  engineering  practice. 

The  returns  have  been  exceedingly  gratifying,  and  especially 
so  has  been  the  spirit  with  which  the  "Questions"  have  been 
received  and  answered. 

Many  requests  have  been  received  from  chief  draftsmen  for 
a  copy  of  the  returns. 

The  questions  submitted  and  the  answers  received  are  given 
somewhat  in  detail  below. 

Q.  i.  Do  you  place  complete  information  for  the  shop  on  the 
pencil  drawing,  such  as  all  dimensions,  notes,  title,  bill  of 
material,  scale,  etc.? 

Complete  information  is  placed  on  drawing  before  tracing.. .  .  57 

Complete  information  is  placed  on  tracing  only 42 

Principal  dimensions  and  title  only  on  pencil  drawing 2 

Draw  directly  on  bond  paper 10 

Did  not  answer  this  question 10 

Sometimes 7 

215 


216  MECHANICAL  DRAWING 

Reasons  given  for  making  the  pencil  drawing  complete: 

To  arrange  notes.     To  save  time.     The  tracing  is  not  usually  made 
by  the  draftsman  who  makes  the  pencil  drawing. 

Q.  2.  Do  you  ever  ink  the  pencil  drawing? 

Never  ink  the  pencil  drawing 91 

Generally  ink  the  pencil  drawing 7 

Sometimes  ink  the  pencil  drawing 8 

Sometimes  ink  the  pencil  drawing  and  shellac  it  for  shop  use .  i 

Use  bond  paper 10 

Make  pencil  drawings  on  dull  side  of  tracing  cloth 2 

Ink  center  lines  of  assembly  drawing i 

Ink  center  lines  of  pencil  drawings  in  red 2 

Q.  3.  Do  you  trace  on  cloth  and  blue  print? 

Always  trace  on  cloth  and  blue  print 102 

Blue  print  from  bond  paper 10 

Blue  print  from  bond  paper  occasionally i 

Sometimes  make  "  Vandyke  "  prints  for  shop  use i 

Sometimes  use  paper  drawings  in  shop  for  jigs  and  fixtures. . .  i 

Q.  4.  Do  you  use  blue  prints  entirely  in  the  shop? 

Use  blue  prints  altogether  in  shop 105 

Sometimes  use  pencil  drawings  or  sketch 21 

Sometimes  use  sketches  made  with  copying  ink 

Sometimes  use  prints  from  "  Vandyke  " 

Use  white  prints  mounted  on  cardboard  and  varnished 

Use  blue  prints  mounted  on  cardboard 

Use  sketches  for  rush  work 

Q.  5.  When  tracing  do  you  use  uniform  wide  object  lines? 
Ever  use  shade  lines? 

Use  uniform,  thick  object  lines.     Never  use  shade  lines ibo 

Sometimes  use  shade  lines 21 

Use  shade  lines  on  small  details 5 

Always  use  shade  lines 14 

Experts  in  the  use  of  shade  lines  may  do  so  to  make  drawings 

clear i 

Shade  rounded  parts i 


PRESENT  PRACTICE  IN  DRAFTING  ROOM  217 
Q.  6.  What  kind  of  a  center  line  do  you  use? 

Long  dash,  very  narrow,  and  dot,  thus: 42 

Long  dash  and  two  dots,  -  29 

Very  fine  continuous  line,  -                                                    —  19 

Very  fine  dash  line,  long  dashes,  —  8 

Long  dash  and  dot  in  red,  -  3 

Continuous  fine  red  line,  —                                                       — -  8 

Long  dash  and  three  dots,  -                                            I 

Long  dash  and  two  dots,  thus: i 


Q.  7.  What  kind  of  dimension  line  do  you  use? 

Continuous  fine  line,  broken  only  for  dimension —     52 

Fine  long  dash  line,  -  32 

Fine  long  dash  line  and  dot,  -                                                —  13 

Fine  continuous  red  line,  -  8 

Fine  continuous  blue  line,  —  4 

Fine  continuous  green  line.  —  i 

Same  character  of  line  as  center  line, 2 

Dotted  line, i 

Long  dash  and  two  dots,  —                                                     —  2 

Heavy  broken  line, i 


Q.  8.  What  style  of  lettering  do  you  use?  Sloping?  Vertical? 
Free-hand?  All  capitals  of  uniform  height?  or  capitals 
and  lower  case? 

Free-hand  sloping ' 52 

Free-hand  vertical 45 

Free-hand  capitals,  Gothic,  uniform  height 61 

Free-hand  capitals, 'and  lower  case 40 

All  caps,  initials  slightly  higher 5 

Lettering  left  to  option  of  draftsman 2 

Mechanical  lettering,  all  caps 3 

Not  particular,  the  neatest  the  draftsman  can  make  free  hand  4 

Mechanical  lettering,  all  caps,  sloping 2 

Give  great  latitude  in  lettering,  only  insist  it  be  bold  and  neat  i 

Roman,  caps  and  lower  case,  free  hand 2 

Large  letters  Aths,  small  ^-ds  and  |th 2 


218  •  MECHANICAL  DRAWING 

Q.  9.  Are  your  titles  and  bills  of  material  printed  or  lettered  by 
hand? 

Lettered  by  hand 79 

Standard  titles  printed  and  filled  in  by  hand 12 

Bill  of  material  table  printed  and  lettered  by  hand 12 

Lettered  by  hand,  contemplate  having  them  printed i 

B.  of  M.  typewritten  on  separate  sheet  and  blue  printed 8 

Titles  partly  printed  and  filled  in  by  hand 8 

Use  rubber  stamp  for  standard  title,  fill  in  by  hand 6 

Standard  title,  bill  of  material  lithographed  on  tracing  cloth  8 


Q.  10.  Do  you  use  a  border  line  on  drawings? 

Always  use  border  lines \  ; 97 

Never  use  border  lines 13 

Use  border  lines  on  foundation  plans,  to  send  out 

No  border  lines  on  detail  drawings 

Intend  to  discontinue  the  use  of  border  lines 

Border  lines  used  only  on  design  drawings 

Only  on  drawings  to  be  mounted  on  cardboard 

Only  used  for  trimming  blue  print 2 

On  assembly  drawings  only . i 

Width  of  margins  reported:     i",  J",  f  ",  1",  and  i". 


Q.  ii.  When   hatch-lining   sections,    do   you   use   uniform   or 
symbolic  hatch  lines? 

Standard  symbolic  lines • 59 

Uniform  hatch  lines  for  all  materials 44 

Shade  section  part  with  4H  pencil  and  note  name  of  material  4 

Symbolic  hatch  lines  and  add  name  of  material 3 

Uniform  hatch  lines  for  metal  only i 

Uniform  on  details,  symbolic  on  assembly  drawings 5 

Pencil  hatch  on  tracings  and  note  material  other  than  cast  iron  i 

Uniform  hatch  lines,  sometimes  solid  shading .,  i 

No  uniform  system i 

Sections  tinted  with  water  colors  representing  the  metals ....  i 


PRESENT  PRACTICE  IN  DRAFTING  ROOM  219 

Q.  12.  Is  the  pencil  drawing  preserved?     Is  the  tracing  stored 

or  do  you  make  "Vandyke"  prints  for  storing  away? 

Store  tracings  only 96 

Pencil  drawings  preserved  for  a  time 30 

Pencil  drawings  preserved 3 

White  prints  made  and  bound  for  reference i 

Tracings  kept  in  office  for  reference,  blue  prints  stored 9 

"  Vandyke  "  prints  stored i 

Use  "  Vandyke  "  as  substitute  for  tracing 2 

Arrangement   drawings  preserved,  detail  drawings  destroyed 
after  job  is  completed.     Pencil  drawings  used  for  gasket 

paper....  i 

Original  pencil  drawing  inked  and  stored i 

Assembly  drawings  and  layouts  preserved 4 

Patent  office  drawings  preserved i 

Tried  "  Vandyke  "  but  found  it  unserviceable,  tearing  easily.  .  i 


Q.  13.  Do  you  use  6H  grade  of  pencil  for  pencil  drawings  or 
what? 

6H 73 

4H,  mostly  for  figures  and  letters 52 

5H 16 

Ranging  from  2H  to  8H 53 


Q.  14.  Do  you  use  plain  orthographic  projection  for  free-hand 
sketches?  Ever  use  perspective  or  isometrical  drawing 
for  sketches? 

Plane  orthographic  3d  angle  projection 99 

Insometrical  drawing  for  sketches 25 

Perspective  for  sketches .  .  .  .- i 

Isometric  for  piping  layouts  and  similar  work 8 

Perspective  and  isometric  for  catalogue  work 2 

Isometric  sometimes 6 

Never  use  free-hand  sketches 6 

One  says,  "When  we  run  into  other  than  orthographic,  men  are  too 
timid  and  not  sure  of  themselves.  In  perspective  drawings  when  work  is 
cylindrical,  workmen  get  mixed  up  on  center  lines. 


220  MECHANICAL  DRAWING 

Q.  15.  What  sizes  of  sheets  do  you  use  for  drawings? 

9"  Xi  2" 13 

i2"Xi8" 16 

i8"X24" 20 

24"X36" 19 

There  seems  to  be  little  uniformity  in  the  sizes  of  shop  drawings,  about 
67  firms  reporting  different  combinations;  A  few  have  no  system  but 
simply  make  the  size  of  sheet  to  suit  the  object  to  be  drawn. 


Q.  1 6.  Do  you  use  red  ink  on  tracings? 

Never  use  red  ink  on  tracings 57 

Recently  discarded  the  use  of  red  ink 2 

Use  red  ink  for  pattern  figures i 

Use  red  ink  for  center  and  dimension  lines 8 

Use  red  ink  for  check  marks i 

Use,  red  ink  for  existing  work  on  studies i 

Use  red  ink  sometimes 2 

Use  red  ink  on  occasions  when  it  is  desired  to  show  old  work 

in  red  and  new  work  in  black  (use  carmine) i 

Use  carmine  for  brick .  .  i 


Qs.   17  and  27.     How  indicate  finished  surfaces  on  drawings? 
When  finished  all  over?     When  "file  finished,"  ground 
planed,  bored,  drilled,  etc.? 

Finished  surfaces  indicated  as  in  Fig.  i '. 65 

Finished  surfaces  indicated  as  in  Fig.  2 16 

Finished  surfaces  indicated  as  in  Fig.  3 8 

Finished  surfaces  indicated  as  in  Fig.  4 2 

Finished  surfaces  indicated  as  in  Fig.  5 2 

Bound  the  surfaces  with  red  lines 2 

Bound  the  surfaces  with  dotted  lines 2 

Name  the  finish  by  note  in  full 68 

Do  not  specify  machinery  method 6 

(See  drawing.) 


PRESENT  PRACTICE  IN  DRAFTING  ROOM 


221 


Q.  1 8.  Do  you  use  horizontal  or  sloping  lines  for  convention 
in  screw  threads? 

Sloping  lines,  see  Fig.  6 94 

Horizontal  lines,  see  Fig.  7 12 


flG.S. 


^=ea 


FIG.  6. 


FIG.  7. 


FIG.  8. 


It! 


FIG.  9. 


FIG.  10. 


Horizontal  lines,  see  Fig.  8 13 

Both 7 

Neither,  but  as  shown  in  Fig.  9 i 

Neither,  but  as  shown  in  Fig.  10 i 


222 


MECHANICAL  DRAWING 


Q.  19.  When  a  large  surface  is  in  section  do  you  hatch-line 
around  the  edges  only? 

Hatch-line  edges  only 62 

Sometimes 3 

Hatch  section  all  over 54 

Do  not  use  hatch  lines;  shade  the  whole  surface  with  ^.H  pencil  3 

Usually  show  a  broken  surface  line i 


F/G.//. 


Q.  20.  Do  you  section  keyways  in  hubs  or  show  by  invisible 
lines? 

Section  keyways  as  shown  in  Fig.  1 1 73 

Show  key  way  by  invisible  lines,  see  Fig.  12 40 

Keyways  in  hubs  left  blank i 


Q.  21.  In  dimensioning  do  you  prefer  to  place  the  dimension 
upon  the  piece  or  outside  of  it? 

Outside  whenever  possible 92 

Upon  the  piece 13 

Both,  according  to  size  and  shape  of  part 19 

No  rule i 

Commenting  on  placing  dimensions  outside  of  piece  one  says,  "It  entails 
less  confusion  to  workman."  Another  says:  "So  as  to  make  detail  stand 
out." 


PRESENT  PRACTICE  IN  DRAFTING  ROOM  223 

Q.  22.  Do  you  use  feet  and  inches  over  24  inches? 

Yes 69 

Use  feet  and  inches  over  36" 4 

Use  feet  and  inches  over  24"  on  foundations  and  outlines. ...  2 

Use  feet  and  inches  over  48" 6 

All  inches 21 

For  pulleys  use  inches  up  to  48" i 

Inches  up  to  10  feet 2 

Start  feet   24"  thus:     2-Lo" 2 

Usually,  but  not  always 2 

Yes,  except  pitch  diameters  of  gears,  which  are  all  given  in 

inches 2 

Yes,  except  in  boiler  and  sheet  iron  work 3 

Use  feet  and  inches  over  1 2" 6 

Inches  up  to  100" 3 

Inches  up  to  60" i 

Q.  23.  How  do  you  indicate  feet  and  inches?     Thus  2  ft.  4", 

or  thus  2-1-4"? 
2-L-4"— 97,  2FT-  4"— 5,  2  FT.  4"—  2,  2ft.  4"— 13.    Both  2ft.  4"  and 

2-4" — I,  2FT.  4  IN. —  I,  2'  4" — 8,  2^  4^ — I. 

Q.  24.  Do  you  dimension  the  same  part  on  more  than  one  view? 

One  view 94 

More  than  one  view  as  check .' 46 

Q.  25.  When  several  parts  of  a  drawing  are  identical  would  the 
dimensioning  of  one  part  suffice  for  all,  or  would  you 
repeat  the  dimension  on  each  part? 

One  part  only 82 

Would  repeat  or  indicate  by  note 39 

"Left  to  judgment  of  draftsman" i 

"  When  it  is  evident'  that  several  parts  are  identical  the  dimensioning 
of  one  part  would  suffice,  '  Would  never  leave  room  for  doubt.'  " 

Q.  26.  Do  you  write  R  for  radius  or  RAD.?  D.  for  diameter 
or  DIA.? 

RAD 35    Rad 47    R 32     rad i    r 3 

DIA 41    Dia 48    D 15    d 3    dia 4 

DIAM i    Diam 3    diam 5 

Do  not  use  R.  or  RAD.,  dimension  only i 


224  MECHANICAL  DRAWING 

Q.  28.  Do  you  always  give  number  of  threads  per  inch?    When 
you  do  how  are  they  indicated? 

Only  give  number  of  threads  when  not  standard 67 

All  others  always  indicate  number  of  threads  in  a  great  variety  of  ways. 
A  few  of  the  different  styles  of  noting  the  threads  are  given  below: 

f" — 10  Thr.  5THDS.  PER  i".  Sthds.  4  threads  per  inch.  Mach. 
Screw  10-24,  ii"  XII,  16  P.  RH.  Vth.  U.  S.  S.  XVIII,  i"-8- 
U.  S.  S.  i"  TAP,  8  PITCH,  3  TH'D  R.  H.  SQ.  DOUBLE,  $"-18  THDS. 

R.  H.  OWN  ST'D  io  thds.  per  inch.     For  pipe  tap  thus,  \"  P.T.,  etc.,  etc. 

Q.  29.  How  do  you  "Mark"  a  piece  to  indicate  on  the  bill  of 
material? 

Number  it  on  drawing  and  put  a  circle  around  it 34 

By  name  or  letter 35 

By  patron  number 2 

By  symbol  and  number 14 

Castings,  I,  II,  III,  Forgings,  i,  2,  3. 

Q.  30.  When   a   working   drawing   is   fully   dimensioned   why 
should  the  scale  be  placed  on  the  drawing? 

For  convenience  of  drafting  room 25 

Check  against  errors 1 1 

Not  necessary 18 

Scale  not  placed  on  shop  drawings 18 

For  convenience  in  calculations  and  planimeter  work i 

To  give  an  idea  of  over-all  dimensions  when  these  are  not 
given.      "  We    never    saw  a  drawing  so  fully  dimensioned 

as  to  warrant  leaving  off  the  scale  " 2 

"  If  a  drawing  is  to  scale  the  scale  should  be  on  the  drawing,  whether 

it  is  needed  or  not." 

"  It  gives  every  one  interested  a  better  conception  of  the  proportions 

of  the  piece,  and  there  are  frequently  portions  of  a  design  which  do  not 

require  a  dimension  for  the  shop  to  work  to,  and  which  it  is  interesting  to 

scale  from  an  engineering  point  of  view." 

"  To  get  approximate  dimensions  not  given  on  drawing." 

"  Impractical  to  dimension  all  measurements  for  all  classes  of  work." 

"  Scale  will  tell  at  a  glance,  dimensions  would  have  to  be  scaled." 

"  To  obtain  an  idea    of  relative  size  of  parts  without  scaling  the 

drawings." 


PRESENT  PRACTICE  IN  DRAFTING  ROOM  225 

"  To  sketch  on  clearance."  "  To  proportion  changes."  "  When 
erecting  to  measure  over-all  sizes." 

"  In  case  a  dimension  has  been  left  off,  the  scale  will  help  out." 

"  This  is  a  question  of  opinion;  some  will  not  have  the  scale,  others 
insist  on  it."  "  We  always  give  the  scale." 

"  It  is  an  immense  help  and  time  saver  in  the  drawing  room." 

"  Generally  no  reason.  In  our  work  we  combine  standard  apparatus 
by  'fudge'  tracing,  and  it  is  convenient  to  know  scale  so  all  parts  will  surely 
be  to  same  scale." 

"  In  discussing  alterations,  additions,  clearances,  etc.,  it  is  convenient 
to  know  the  scale  instantly." 

"  For  convenience  in  drafting  room.  We  often  put  an  arbitrary  scale 
on  with  a  reference  letter  indicating  scale  to  draftsman." 

"  To  give  toolmaker  an  idea  of  the  size  of  the  finished  piece." 

"  As  an  aid  to  the  eye  in  reading." 
Above  are  some  of  the  reasons  given  for  placing  the  scale  on  the  drawing. 

Below  are  given  a  few  of  the  reasons  why  some  do  not  place  the  scale 

on  the  drawing. 

"  Scale  should  never  be  used  in  shop,"  says  one. 

"  Not  necessary.     Sometimes  drawing  is  made  out  of  scale." 

"  Not  advisable,  on  account  of  workmen  getting  into  the  habit  of 
working  to  scale  instead  of  to  the  figures." 

"  Know  of  no  good  reason  at  all." 

"  Believe  it  best  to  leave  scale  off." 

"  Should  not.    Drawing  should  never  be  scaled." 

"  Know  of  no  good  reason  why  it  should  be." 

"  Should  not  be  given  on  drawing." 

"  Do  not  object  if  left  off,  not  needed." 

Q.  31.  Do  you  use  the  glazed  or  dull  side  of  tracing  cloth? 
Dull  side 66        Glazed  side.  .32        Both 4 

"  Dull  side,  because  it  lies  flat  better  in  drawers." 

"  Dull  side,  so  that  changes  which  may  be  necessary  while  work  is 
under  construction,  can  be  made  easily  in  pencil  and  later  in  ink." 

"  Dull  side  so  tracings  may  be  checked  in  pencil." 

"  It  prevents  curling." 

"  Both,  although  the  glazed  side  when  traced  on  lies  better  in  the 
drawer." 

"  We  use  cloth  glazed  on  both  sides,  work  on  convex  side,  so  that 
shrinkage  of  ink  will  eliminate  camber." 

"  Dull,  except  for  U.  S.  Government,  who  requires  the  glazed  side 
to  be  used." 


226  MECHANICAL  DRAWING 

Q.  32.  How  do  you  place  pattern  numbers  on  castings? 

Pattern  number  with  symbol  or  letter  is  placed  on  or  near  the 
piece,  e.g.,  PATT.-D-478-C 36 

This  question  was  not  happily  stated:  most  answers  gave  "raised 
letters  cast  on,"  while  the  question  like  all  the  others  refers  to  the  marking 
of  the  drawing. 

Q.  33.  How  do  you  note  changes  on  a  drawing? 

On  tracing  with  date 32 

New  tracing  and  new  number 17 

Put  a  circle  around  old  figure  and  write  new  figure  beside  it 

with  date 8 

Make  new  tracing 5 

Red  ink  with  date 8 

Use  rubber  stamp  "Revised  "  with  date,  and  indicate  changes 

on  record  print 28 

Use  change  card  system i 

Special  forms  for  purpose.  Change  made  in  a  book  with 

date.    New  prints  made  to  replace.     In  place  at  title 

with  draftsman's  initials  and  date .  .  8 


Q.  34.  Do  you  place  dimensions  to  read  from  bottom  and  right 
hand,  or  all  to  read  from  bottom,  or  how? 

Bottom  and  right  hand ....  103     From  bottom  only 2 

No  fixed  rule 2 

From  R  to  L  and  bottom  to  top i 


Q.   35.  Do  you  always  make  a  table  to  contain  the  bill  of 
material? 

Yes 49    No 25    Not  always 5 

Usually i     Use  separate  bill 32 

Bills  on  general  drawings  only.     On  details  number  is  marked  on  piece. 
"  No,  but  it  is  advisable  to  do  so."    "  Have  abandoned  that  system." 


INDEX 


A 

PACE 

Angle,  To  Bisect  an 50 

Angle,  To  Construct  an 18 

Anti-friction  Curve,  " Schiele's" 177 

Arkansas  Oil-stones.  .  16 


B 

Bill  of  Material 23,  147 

Board,  Drawing i 

Border  Lines , 27 

Bow  Instruments 12 

Breaks,  Conventional 29 

Brilliant  Points 196 

C 

Celluloid,  Sheet  of  Thin 175 

Center  Lines 25,  -217 

Circle,  Arc  of  a,  To  Draw  a  Line  Tangent  to  an 168 

Circle,  Arc  of  a,  To  Find  the  Center  of  an , 63 

Circle,  To  Construct  the  Involute  of  a 63 

Circle,  To  Draw  an  Arc  of  a,  Tangent  to  a  Straight  Line  and  a  Circle 172 

Circle,  To  Draw  an  Arc  of  a,  Tangent  to  Two  Circles 171 

Circle,  To  Draw  ah  Arc  of  a,  Tangent  to  Two  Straight  Lines 170 

Circle,  To  Draw  a  Right  Line  Equal  to  Half  the  Circumference  of  a 58 

Circle,  To  Draw  a  Tangent  between  Two 169 

Circle,  To  Draw  Tangents  to  Two 170 

Circle,  To  Find  the  Length  of  an  Arc  of  a,  Approximately 175 

Circle,  To  Inscribe  a,  within  a  Triangle 1 70 

Cissoid,  To  Draw  the 177 

Compass 10 

Complete  Information  on  Pencil  Drawing 215 

Connecting  Rods 131,  149 

Conventional  Breaks 29 

Conventional  Lines 24 

Conventions,  Drafting  Room  Standard 22 

Conventions,  Shading 194 

227 


228  INDEX 

PAGE 

Cross-section  Lines 27 

Curves,  Irregular 19 

Cycloid,  To  Describe  the 1 75,  176 


D 

Dark  Surfaces 194 

Development  of  a  Locomotive  Gusset  Sheet 187 

Development  of  the  Surface  of  a  Cone 123, 125 

Development  of  the  Surface  of  a  Cylindrical  Dome 186 

Development  of  the  Surface  of  a  Right  Cylinder 122 

Development  of  the  Surfaces  of  a  Hexagonal  Prism 119 

Development  Problems .' 119 

Dihedral  Angles 81 

Dimensioning  Drawings 147,  222 

Dimension  Lines 25,  217 

Direction,  The,  of  the  Rays  of  Light 195 

Dividers,  Hair-spring 13 

Drafting-room  Conventions 22,  215 

Drawing-board i 

Drawing  Paper 22 

Drawing-pen 14 

Drawing  to  Scale 16 

Drawings,  Sizes  of  Sheets 22 


E 

I 

Ellipse,  Given  an,  to  Find  the  Axes  and  Foci 173 

Ellipse,  To  Describe  an 64 

Epicycloid,  To  Describe  an  Interior 178 

Epicycloid,  To  Describe  the 69, 177 

Equilateral  Triangle,  To  Construct  an .,    54 

Examples  of  Working  Drawings 149,  150,  151 


F 

Figuring  and  Lettering 46,  74 

Finish  Indications 29,  221 


G 

Geometrical  Drawing 44 

Geometrical  Drawing  Problems « 48 

Glass-paper  Pencil  Sharpener 19 

Gothic  Letters 61 

Grade  of  Pencils 7 


INDEX  229 


H 

PAGE 

Hatch  Lines 27 

Heptagon,  To  Construct  a 55 

Hyperbola,  To  Draw  an 68 

Hypocycloid,  To  Describe  the 69 


I 

Ink  Eraser 20 

Inking  the  Pencil  Drawing 216 

Ink 21 

Instruments 9 

Intersection  Problems 118,  210 

Intersection,  The,  of  a  Cylinder  with  a  Cone 124 

Intersection,  The,  of  a  Plane  with  an  Irregular  Surface  of  Revolution 192 

Intersection,  The,  of  Two  Cylinders 127 

Involute,  of  a  Circle,  To  Construct  the 63 

Isometrical  Cube 128 

Isometrical  Drawing 128 

Isometrical  Drawing,  Examples  of 130,  133 

Isometrical  Drawing  of  a  Hollow  Cube 140 

Isometrical  Drawing  of  a  Two-armed  Cross 135 

Isometrical  Problems 135,  143 

Isometrical  Scale,  The 129 


L 

Lettering 46 

Lettering  and  Figuring 74 

Lettering,  Style  of 22 

Line  of  Section 27 

Line  of  Shade 194 

Line,  To  Divide  a 50 

Line,  To  Draw  a,  Parallel  to  Another ....'. 164 

Lines • 216,  217 


M 

Model  of  the  Co-ordinate  Planes. . .  82 


N 

Notation 89 

Notes  on  Drawings 226 


230  INDEX 


O 

PAGE 

Octagon,  To  Construct  an 56 

Orthographic  Projection 81 

Oval,  To  Construct  an 69 


P 

Paper 21 

Parabola,  To  Construct  a 66 

Pencil 7 

Pencil  Drawings 147,  216 

Pencil  Eraser 20 

Pencil,  To  Sharpen  the , 7 

Pen,  Drawing 14 

Pen,  to  Sharpen  the  Drawing 15 

Pentagon,  To  Construct  a 56 

Perpendicular,  to  Erect  a 163, 164 

Planes  of  Projection,  The 81 

Polygon,  To  Construct  a • 57 

Problems  in  Geometrical  Drawing 44 

Problems  in  Intersections 118,  192,  210 

Problems  in  Isometrical  Drawing 135 

Problems  in  Mechanical  Drawing 145 

Projection  of  the  Helix  as  Applied  to  Screw-threads 190,  191 

Projection,  The,  of  Plane  Surfaces 100 

Projection,  The,  of  Solids 119 

Projection,  The,  of  Straight  Lines 94 

Projection,  The,  of  the  Cone 210 

Proportional,  To  Find  a  Mean,  to  Two  Given  Lines 58 

Proportional,  To  Find  a  Fourth,  to  Three  Given  Lines 168 

Protractor .  .  18 


R 

Rays  of  Light 194 

Rays,  Visual 194 

Rhomboid,  To  Construct  the 52 

Right  Angle,  To  Trisect  a 54 

Roman  Letters 158 


S 

Scale,  Drawing  to 16,  178 

Scale  on  Drawings 224 

Scale,  To  Construct  a 178, 


INDEX  231 

PAGE 

Schiele's  Curve,  To  Draw ., 177 

Section  Lines % 27 

Section  Lines,  Standard 28 

Shade  Lines 194 

Shade  Lines  and  Shading 196 

Shade,  To,  a  Concave  Cylindrical  Surface 199 

Shade,  To,  the  Elevation  of  a  Sphere 198 

Shade,  To,  a  Right  Cone 200 

Shade,  To,  a  Right  Cylinder 199 

Shadows , 200 

Sharpen  Pen,  To 15 

Sharpen  Pencil,  To 7 

Sheet  Celluloid 175 

Source  of  Light .  194 

Spiral,  To  Describe  the 1 74 

Square  Thread 190,  191 

Square,  To  Construct  a 165 

Stippling - 198 


T 

Tacks,  Thumb * 21 

Third  Dihedral  Angle 81,  82,  83,  86 

Title,  Standard.  .  . 146 

Title,  The,  of  a  Working  Drawing ; 146 

Titles 218 

Tracing  Cloth 148,  225 

Triangles 4 

Triangle,  To  Construct  a 54 

Triangular  Scale 17 

T-square i 

Type  Specimens 163 

U 

Use  of  Compasses 10 

Use  of  Dividers  or  Spacers 13 

Use  of  Drawing-board i 

Use  of  Drawing-pen 14 

Use  of  Instruments 10 

Use  of  Irregular  Curves 19 

Use  of  Pencil 7 

Use  of  Protractor 18 

Use  of  Scale 17 

Use  of  Spring  Bows 12 

Use  of  Triangles 5 

Use  of  T-square i 


232  INDEX 


PAGE 

Visual  Rays , T94 

Volute,  To  Describe  the  "Ionic" 67 

W 

Working  Drawings: J4S 

Working  Drawings,  Examples  of *49)  IS° 

Working  Drawings,  Method  of  Making 145 

Working  Drawing,  What  is  a J45 

Writing-pen 23 


Wiley  Special  Subject  Catalogues 

For  convenience  a  list  of  the  Wiley  Special  Subject 
Catalogues,  envelope  size,  has  been  printed.  These 
are  arranged  in  groups — each  catalogue  having  a  key 
symbol.  (See  special  Subject  List  Below).  To 
obtain  any  of  these  catalogues,  send  a  postal  using 
the  key  symbols  of  the  Catalogues  desired. 


1— Agriculture.     Animal  Husbandry.    Dairying.     Industrial 
Canning  and  Preserving. 

2 — Architecture.       Building.      Masonry. 

3 — Business  Administration  and  Management.     Law. 

Industrial  Processes:   Canning  and  Preserving;    Oil  and  Gas 
Production;  Paint;  Printing;  Sugar  Manufacture;  Textile. 

CHEMISTRY 
4a  General;  Analytical,-  Qualitative  and  Quantitative;  Inorganic; 

Organic. 
4b  Electro-  and  Physical;  Food  and  Water;  Industrial;  Medical 

and  Pharmaceutical;  Sugar. 

CIVIL  ENGINEERING 

5a  Unclassified  and  Structural  Engineering. 

5b  Materials  and  Mechanics  of  Construction,  including;  Cement 
and  Concrete;  Excavation  and  Earthwork;  Foundations; 
Masonry. 

5c  Railroads;  Surveying. 

5d  Dams;  Hydraulic  Engineering;  Pumping  and  Hydraulics;  Irri- 
gation Engineering;  River  and  Harbor  Engineering;  Water 

Supply. 

(Over) 


CIVIL  ENGINEERING—  Continued 

5e  Highways;  Municipal  Engineering;  Sanitary  Engineering; 
Water  Supply.  Forestry.  Horticulture,  Botany  and 
Landscape  Gardening. 


6 — Design.  Decoration.  Drawing:  General;  Descriptive 
Geometry;  Kinematics;  Mechanical. 

ELECTRICAL  ENGINEERING— PHYSICS 

7 — General  and  Unclassified;  Batteries;  Central  Station  Practice; 
Distribution  and  Transmission;  Dynamo-Electro  Machinery; 
Electro-Chemistry  and  Metallurgy;  Measuring  Instruments 
and  Miscellaneous  Apparatus. 


8 — Astronomy.      Meteorology.      Explosives.      Marine    and 
Naval  Engineering.     Military.     Miscellaneous  Books. 

MATHEMATICS 

9 — General;    Algebra;   Analytic  and   Plane   Geometry;    Calculus; 
Trigonometry;  Vector  Analysis. 

MECHANICAL  ENGINEERING 

lOa  General  and  Unclassified;  Foundry  Practice;  Shop  Practice. 
lOb  Gas  Power  and    Internal   Combustion  Engines;  Heating  and 

Ventilation;  Refrigeration. 
lOc   Machine  Design  and  Mechanism;  Power  Transmission;  Steam 

Power  and  Power  Plants;  Thermodynamics  and  Heat  Power. 
1 1 — Mechanics. 

12 — Medicine.  Pharmacy.  Medical  and  Pharmaceutical  Chem- 
istry. Sanitary  Science  and  Engineering.  Bacteriology  and 

Biology. 

MINING  ENGINEERING 

13 — General;  Assaying;  Excavation,  Earthwork,  Tunneling,  Etc.; 
Explosives;  Geology;  Metallurgy;  Mineralogy;  Prospecting; 
Ventilation. 


THIS  BOOK  IS  DUE  ON  THE  LAST  DATE 
STAMPED  BELOW 


AN  INITIAL  FINE  OF  25  CENTS 

WILL  BE  ASSESSED  FOR  FAILURE  TO  RETURN 
THIS  BOOK  ON  THE  DATE  DUE.  THE  PENALTY 
WILL  INCREASE  TO  5O  CENTS  ON  THE  FOURTH 
DAY  AND  TO  $1.OO  ON  THE  SEVENTH  DAY 
OVERDUE. 


JUL    88  1939 


us? 


±* 


REC'L*  LID 


mtt 


LD21-20m-5,'39  (9269s) 


9724 


UNIVERSITY  OF  CALIFORNIA  LIBRARY 


